Input files for Expert mode¶
In this section, detailed input files (*.def) are explained. Input files are categorized by the following six parts. The files that are listed in parentheses correspond to the file made by vmcdry.out.
List:
No keyword (namelist.def): This file is a list of input file names with keywords. Each keywords is fixed, but file names are free to be determined.
Basic parameters:
ModPara (modpara.def): Set the parameters for basic parameters such as site number, electron number, Lanczos step etc. LocSpin (locspn.def): Set the location of local spin.
Hamiltonian:
Hamiltonian for mVMC is denoted by
\[\begin{split}\begin{aligned} {\cal H}&={\cal H}_T+{\cal H}_U+{\cal H}_V+{\cal H}_H+{\cal H}_E+{\cal H}_P+{\cal H}_I,\\ {\cal H}_T&=-\sum_{i, j}\sum_{\sigma_1, \sigma_2}t_{ij\sigma_1\sigma_2} c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\\ {\cal H}_U&=\sum_{i} U_i n_ {i \uparrow}n_{i \downarrow},\\ {\cal H}_V&=\sum_{i,j} V_{ij}n_ {i}n_{j},\\ {\cal H}_H&=-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}),\\ {\cal H}_E&=\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow}+c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}),\\ {\cal H}_P&=\sum_{i,j}J_{ij}^{\rm Pair} c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow},\\ {\cal H}_I&=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}, \end{aligned}\end{split}\]as the format of interactions for electron system. Here, we define the charge density operator with spin \(\sigma\) at site \(i\) as \(n_{i \sigma}=c_{i\sigma}^{\dagger}c_{i\sigma}\) and the total charge density operator at site \(i\) as \(n_i=n_{i\uparrow}+n_{i\downarrow}\). Each parameters are specified by the following files, respectively;
Trans (trans.def): \(t_{ij\sigma_1\sigma_2}\) in \({\cal H}_T\),
CoulombIntra (coulombintra.def): \(U_i\) in \({\cal H}_U\),
CoulombInter (coulombinter.def): \(V_{ij}\) in \({\cal H}_V\),
Hund (hund.def): \(J_{ij}^{\rm Hund}\) in \({\cal H}_H\),
Exchange (exchange.def): \(J_{ij}^{\rm Ex}\) in \({\cal H}_E\),
PairHop: \(J_{ij}^{\rm Pair}\) in \({\cal H}_P\),
InterAll: \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\) in \({\cal H}_I\).
t-J model input convention
For a t-J model with the physical convention
\[{\cal H}_{tJ} = -\sum_{i,j,\sigma} t_{ij} {\tilde c}_{i\sigma}^{\dagger}{\tilde c}_{j\sigma} + \sum_{i,j} J_{ij}\left({\boldsymbol S}_i\cdot{\boldsymbol S}_j - \frac{1}{4}n_i n_j\right),\]where the tilde denotes the no-double-occupancy Hilbert space, use the
Trans,CoulombInter,Hund, andExchangefiles; this is not anInterAllinput. With the sign convention of the Hamiltonian above, a positive physical coupling \(J_{ij}\) is represented by\[V_{ij}=-\frac{J_{ij}}{4}, \qquad J_{ij}^{\rm Hund}=-\frac{J_{ij}}{2}, \qquad J_{ij}^{\rm Ex}=-\frac{J_{ij}}{2}.\]The t-J update path must also be selected by
NExUpdatePathinmodpara.def. The current t-J update paths do not supportBackFloworLocSpininputs. Since double occupancy is excluded, the electron number must not exceed the number of sites. ForNExUpdatePath=4, spin hopping needs at least one empty site, soNcond < Nsite(or2*Nelectron < Nsite) is required. ForNExUpdatePath=5,Ncond <= Nsite(or2*Nelectron <= Nsite) is allowed.Variational parameters to be optimized:
The variational parameters to be optimized are specified by using this categorized files. In mVMC, the variational wave function is given as
\[\begin{split}\begin{aligned} |\psi \rangle &= {\cal N}_{General RBM} {\cal P}_G{\cal P}_J{\cal P}_{SJ}{\cal P}_{d-h}^{(2)}{\cal P}_{d-h}^{(4)}{\cal L}^S{\cal L}^K{\cal L}^P |\phi_{\rm pair} \rangle,\\ {\cal P}_G&=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right],\\ {\cal P}_J&=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right],\\ {\cal P}_{SJ}&=\exp\left[\sum_{i<j} v^s_{ij} m_i m_j\right],\\ {\cal P}_{d-h}^{(2)}&= \exp \left[ \sum_t \sum_{n=0}^2 (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right],\\ {\cal P}_{d-h}^{(4)}&= \exp \left[ \sum_t \sum_{n=0}^4 (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right],\\ {\cal N}_{\rm General RBM}&= \exp \left[ \sum_i a_{i\sigma} n_{i\sigma} \right] \prod_k^{N_h} \cosh \left[ b_k + \sum_{i\sigma} W_{i\sigma k} n_{i\sigma} \right],\\ {\cal L}_S&=\frac{2S+1}{8 \pi^2}\int d\Omega P_s(\cos \beta) \hat{R}(\Omega),\\ {\cal L}_K&=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R},\\ {\cal L}_P&=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha},\end{aligned}\end{split}\]where \(\Omega=(\alpha, \beta, \gamma)\) is the Euler angle, \(\hat{R}(\Omega)\) is the rotational operator, \(P_S(x)\) is the \(S\)-th polynomial, \({\boldsymbol K}\) is the momentum operator of the whole system and \(\hat{T}_{\boldsymbol R}\) is the translational operators corresponding to the translational vector \({\boldsymbol R}\), \(\hat{G}_{\alpha}\) is the point group operator, and \(p_\alpha\) is the parity operator, respectively. For the spin Jastrow factor, \(m_i=n_{i\uparrow}-n_{i\downarrow}\). The details of \({\cal P}_{d-h}^{(2)}\) and \({\cal P}_{d-h}^{(4)}\) are shown in [Tahara2008 ]. The one body part of the wavefunction is represented as the pair function of the real space:
\[|\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma_1, \sigma_2}f_{i\sigma_1j \sigma_2} c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle,\]where \(N\) is the number of electrons and \(N_s\) is the number of sites. The setting for optimizing variational parameters or not is given by the following files (the parameters for \({\cal L}_S\) are specified in the ModPara file).
Gutzwiller (gutzwilleridx.def): Set the target parameters \(g_i\) in \({\cal P}_G\) to be optimized.
Jastrow (jastrowidx.def): Set the target parameters \(v_{ij}\) in \({\cal P}_J\) to be optimized.
SpinJastrow (spinjastrow.def): Set the target parameters \(v^s_{ij}\) in \({\cal P}_{SJ}\) to be optimized.
DH2: Set the target 2-site doublon-holon correlation factor \(\alpha_{2nt}^{d(h)}\) in \({\cal P}_{d-h}^{(2)}\) to be optimized.
DH4: Set the target 4-site doublon-holon correlation factor \(\alpha_{4nt}^{d(h)}\) in \({\cal P}_{d-h}^{(4)}\) to be optimized.
GeneralRBM_PhysLayer: Set the target variational parameters \(a_{i\sigma}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
GeneralRBM_HiddenLayer: Set the target variational parameters \(h_{k}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
GeneralRBM_PhysHidden: Set the target variational parameters \(W_{i\sigma k}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
Orbital/OrbitalAntiParallel (orbitalidx.def): Set the pair orbital with anti-parallel spins \(f_{i\uparrow j\downarrow}\) in \(|\phi_{\rm pair} \rangle\) to be optimized.
OrbitalParallel: Set the pair orbital with anti-parallel spins \(f_{i\sigma j\sigma}\) in \(|\phi_{\rm pair} \rangle\) to be optimized.
OrbitalGeneral: Set the pair orbital with anti-parallel spins \(f_{i\sigma j\sigma'}\) in \(|\phi_{\rm pair} \rangle\) to be optimized.
TransSym (qptransidx.def): Set the the momentum projection operators \({\cal L}_K\) and the lattice translational projection operators \({\cal L}_P\).
Initial variational parameters:
Set the initial values of the variational parameters. When the keyword is not setting, the corresponding parameters are given by random values as default values.
InGutzwiller: Set the initial values of \(g_i\) in \({\cal P}_G\).
InJastrow: Set the initial values of \(v_{ij}\) in \({\cal P}_J\).
InSpinJastrow: Set the initial values of \(v^s_{ij}\) in \({\cal P}_{SJ}\).
InDH2: Set the initial values of \(\alpha_{2nt}^{d(h)}\) in \({\cal P}_{d-h}^{(2)}\).
InDH4: Set the initial values of \(\alpha_{4nt}^{d(h)}\) in \({\cal P}_{d-h}^{(4)}\).
InGeneralRBM_PhysLayer: Set the initial values of \(a_{i\sigma}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
InGeneralRBM_HiddenLayer: Set the initial values of \(h_{k}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
InGeneralRBM_PhysHidden: Set the initial values of \(W_{i\sigma k}\) in the RBM correlation factor \({\cal N}_{\rm General RBM}\).
InOrbital /InOrbitalAntiParallel: Set the initial values of \(f_{i\uparrow j\downarrow}\) in \(|\phi_{\rm pair} \rangle\).
InOrbitalParallel: Set the initial values of \(f_{i\sigma j\sigma}\) in \(|\phi_{\rm pair} \rangle\).
InOrbitalGeneral: Set the initial values of \(f_{i\sigma j\sigma'}\) in \(|\phi_{\rm pair} \rangle\).
Output:
OneBodyG (greenone.def): Set the components of one-body green functions to output.
TwoBodyG (greentwo.def): Set the components of two-body green functions to output.
Twist (twist.def): Set the components of twist operators to output.
Others:
Lattice (lattice.def): Set the position of each site.
List file for Input files (namelist.def)¶
This file determines input filenames correlated with keywords. An example of the file format is shown as follows.
ModPara modpara.def
LocSpin zlocspn.def
Trans ztransfer.def
InterAll zinterall.def
Orbital orbitalidx.def
OneBodyG zcisajs.def
TwoBodyG zcisajscktaltdc.def
File format¶
[string01] [string02]
Parameters¶
[ string01 ]
Type : string-type
Description : Select a word from keywords.
[ string02 ]
Type : string-type
Description : An input filename which is correlated with keywords.
User rules¶
After setting keywords at [string 01], half-width state is needed for writing a filename. You can set the filename freely.
Keywords for input files are shown in Table [Table:Defs].
Essential keywords are “CalcMod”, “ModPara” , “LocSpin”, “Orbital” and “TransSym”.
Keywords can be set in random order.
If keywords or filenames are incorrect, the program is terminated.
When the head of line is
#, the line is skipped.
Keywords |
Details for corresponding files |
|---|---|
ModPara \(^*\) |
Parameters for calculation. |
LocSpin \(^*\) |
Configurations of the local spins for Hamiltonian. |
Trans |
Transfer and chemical potential for Hamiltonian. |
InterAll |
Two-body interactions for Hamiltonian. |
CoulombIntra |
CoulombIntra interactions. |
CoulombInter |
CoulombInter interactions. |
Hund |
Hund couplings. |
PairHop |
Pair hopping couplings. |
Exchange |
Exchange couplings. |
Gutzwiller |
Gutzwiller factors. |
Jastrow |
Charge Jastrow factors. |
SpinJastrow |
Spin Jastrow factors. |
DH2 |
2-site doublon-holon correlation factors. |
DH4 |
4-site doublon-holon correlation factors. |
GeneralRBM_PhysLayer |
A part of the general RBM correlation factor including variational parameters in a physical layer \(\alpha_{i\sigma}\). |
GeneralRBM_HiddenLayer |
A part of the general RBM correlation factor including variational parameters in a hidden layer \(h_{k}\). |
GeneralRBM_PhysHidden |
A part of the general RBM correlation factor including variational parameters which connect physical and hidden layers \(W_{i\sigma k}\). |
Orbital \(^*\) |
Pair orbital factors with anti-parallel spins \(f_{i\uparrow j\downarrow}\). |
OrbitalAntiParallel |
Pair orbital factors with anti-parallel spins \(f_{i\uparrow j\downarrow}\). |
OrbitalParallel |
Pair orbital factors with parallel spins \(f_{i\sigma j\sigma}\). |
OrbitalGeneral |
Pair orbital factors \(f_{i\sigma_1 j\sigma_2}\). |
TransSym \(^*\) |
Translational and lattice symmetry operation. |
InGutzwiller |
Initial values of Gutzwiller factors. |
InJastrow |
Initial values of charge Jastrow factors. |
InSpinJastrow |
Initial values of spin Jastrow factors. |
InDH2 |
Initial values of 2-site doublon-holon correlation factors. |
InDH4 |
Initial values of 4-site doublon-holon correlation factors. |
InGeneralRBM_PhysLayer |
Initial values of variational parameters of the general RBM correlation factors in a physical layer \(\alpha_{i\sigma}\). |
InGeneralRBM_HiddenLayer |
Initial values of variational parameters of the general RBM correlation factors in a hidden layer \(h_{k}\). |
InGeneralRBM_PhysHidden |
Initial values of variational parameters of the general RBM correlation factors which connect physical and hidden layers \(W_{i\sigma k}\). |
InOrbital |
Initial values of pair orbital factors \(f_{i\uparrow j\downarrow}\). |
InOrbitalAntiParallel |
Initial values of pair orbital factors \(f_{i\uparrow j\downarrow}\). |
InOrbitalParallel |
Initial values of pair orbital factors \(f_{i\sigma j\sigma}\). |
InOrbitalGeneral |
Initial values of pair orbital factors \(f_{i\sigma_1 j\sigma_2}\). |
OneBodyG |
Output components for Green functions \(\langle c_{i\sigma}^{\dagger}c_{j\sigma}\rangle\) |
TwoBodyG |
Output components for Correlation functions \(\langle c_{i\sigma}^{\dagger}c_{j\sigma}c_{k\tau}^{\dagger}c_{l\tau}\rangle\) |
Twist |
Output components for Twist operators \(\langle \exp ( i 2\pi \sum_{i\sigma} \sum_{\mu=x,y,z} c^{(\alpha)\mu }_{i\sigma } \mu_{i} n_{i\sigma} ) \rangle\) |
Lattice |
Position of each site. |
ModPara file (modpara.def)¶
This file determines parameters for calculation. An example of the file format is shown as follows.
--------------------
Model_Parameters 0
--------------------
VMC_Cal_Parameters
--------------------
CDataFileHead zvo
CParaFileHead zqp
--------------------
NVMCCalMode 0
NLanczosMode 0
--------------------
NDataIdxStart 1
NDataQtySmp 1
--------------------
Nsite 16
Nelectron 8
NSPGaussLeg 1
NSPStot 0
NMPTrans 1
NSROptItrStep 1200
NSROptItrSmp 100
DSROptRedCut 0.001
DSROptStaDel 0.02
DSROptStepDt 0.02
NVMCWarmUp 10
NVMCInterval 1
NVMCSample 1000
NExUpdatePath 0
RndSeed 11272
NSplitSize 1
NStore 1
File format¶
Lines 1 - 5: Header
Line 6: [string01] [string02]
Line 7: [string03] [string04]
Line 8: Header
Lines 9 - : [string05] [int01] (or [double01])
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : Set a keyword for header of output files.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : Set a header of output files. For example, the output file of one-body green’s functions are named as xxx_cisajs.dat, where xxx is [ string02 ].
[ string03 ]
Type : string-type (blank parameter not allowed)
Description : Set a keyword for header of output files for variational parameters.
[ string04 ]
Type : string-type (blank parameter not allowed)
Description : Set a header of output files for variational parameters. For example, the output file of optimized variational parameters are named as xxx_opt.dat, where xxx is [ string04 ].
[ string05 ]
Type : string-type
Description : Select a word from keywords.
[ int01 ] ([double01])
Type : int (double)-type (blank parameter not allowed)
Description : A parameter which is correlated with a keyword.
User rules¶
From Line 9: After setting keywords at [string 01], a half-width blank is needed for setting a parameter.
From Line 9: When the first character of the line is “-”, the line is not read and skipped.
Keywords and parameters¶
NVMCCalModeType : int-type (default value: 0)
Description : [0] Optimization of variational parameters, [1] Calculation of one body and two body Green’s functions.
NLanczosModeType : int-type (default value: 0)
Description : [0] Not using single Lanczos step, [1] Calculating energy by using Single Lanczos Step, [2] Calculating one body and two body Green’s functions by using Single Lanczos Step (Condition: The options 1 and 2 can be selected when
NVMCCalMode= 1).NDataIdxStartType : int-type (default value: 0)
Description : An integer for numbering of output files. For
NVMCCalMode= 0 ,NDataIdxStartis added at the end of the output files. ForNVMCCalMode= 1, the files are outputted with the number fromNDataIdxStarttoNDataIdxStart+NDataQtySmp-1.NDataQtySmpType : int-type (default value: 1)
Description : The set number for outputted files (only used for
NVMCCalMode= 1).NsiteType : int-type (Positive integer)
Description : The number of sites.
NelectronType : int-type (Positive integer)
Description : The number of electron pairs (the electron number is given by 2
Nelectron).NcondType : int-type (greater than 0)
Description : The number of conduction electrons.
2SzType : int-type
Description : The value of \(2S_z\). Since the electrons form pair, \(2S_z\) must be even number.
NSPGaussLegType : int-type (Positive integer, default value: 8)
Description : The mesh number for the Gauss-legendre quadrature about \(\beta\) integration (\(S_y\) rotation) for the spin quantum-number projection in actual numerical calculation.
NSPStotType : int-type ( greater than 0, default value: 0)
Description : The spin quantum-number.
NMPTransType : int-type (default value: 1)
Description : The absolute value gives the number of the momentum and lattice translational quantum-number projection. When the value is negative, the mode of anti-periodic condition turns on. The quantum-number projection is used from the top to
NMPTranswith the specified weight indicated inTransSymfile. In the case of not applying the projection, this value must be equal to 1.NSROptItrStepType : int-type (Positive integer, default value: 1000)
Description : The whole step number to optimize variational parameters by SR method. Only used for
NVMCCalMode=0.NSROptItrSmpType : int-type (Positive integer, default value:
NSROptItrStep/10)Description : In the
NSROptItrStepstep, the average values of the each variational parameters at theNSROptItrStepstep are adopted as the optimized values. Only used forNVMCCalMode=0.DSROptRedCutType : double-type (default value: 0.001)
Description : The stabilized factor for the SR method by truncation of redundant directions corresponding to \(\varepsilon_{\rm wf}\) in the ref. [Tahara2008 ].
DSROptStaDelType : double-type (default value: 0.02)
Description : The stabilized factor for the SR method by modifying diagonal elements in the overwrap matrix corresponding to \(\varepsilon\) in the ref. [Tahara2008 ].
DSROptStepDtType : double-type
Description : The time step using in the SR method.
NSROptCGMaxIterType : int-type (default value: 0)
Description : The maximum number of CG steps for the SR method. If this is zero or negative, CG steps will be run as many as the size of \(S\) matrix at maximum. Only used for
NSRCG!=0.DSROptCGTolType : double-type (default value: 1.0e-10)
Description : The convergence condition of a CG step in the SR method. CG method runs until the root mean square of the residues becomes below this value. Only used for
NSRCG!=0.NVMCWarmUpType : int-type (Positive integer, default value: 10)
Description : Idling number for the Malkov chain Montecarlo Methods.
NVMCIntervalType : int-type (Positive integer, default value: 1)
Description : The interval step between samples. The local update will be performed
Nsite×NVMCIntervaltimes.NVMCSampleType : int-type (Positive integer, default value: 1000)
Description : The sample numbers to calculate the expected values.
NExUpdatePathType : int-type (Non-negative integer)
Description : The option for local updates. The choices are 0: hopping, 1: exchange or hopping, 2: exchange, 3: KondoGC update (hopping or exchange/local-spin-flip), 4: t-J spin hopping, 5: t-J update (exchange or spin hopping), and 6: doublon-only sampling by pair hopping. The choice between 4 and 5 selects the local-update path for the t-J Hilbert space; it is not the switch for \(S_z\) conservation. The spin sector is specified separately, for example by
2Szin fixed-\(S_z\) calculations. For the t-J choices 4 and 5,BackFlowandLocSpinare not supported. Since double occupancy is excluded, the electron number must not exceedNsite. In addition,NExUpdatePath=4requires at least one empty site for spin hopping, soNcond < Nsite(or2*Nelectron < Nsite) is required.NExUpdatePath=5allowsNcond <= Nsite(or2*Nelectron <= Nsite). ForNExUpdatePath=6, the sampled local states are restricted to empty and doublon states, \((n_{\uparrow}, n_{\downarrow})=(0,0)\) or \((1,1)\). This mode requires0 < Ne < Nsiteand an anti-parallel-spinOrbitalinput. It currently does not supportLocSpin,BackFlow, RBM, orOrbitalGeneral/FSZ inputs.RndSeedType : int-type
Description : The initial seed of generating random number. For MPI parallelization, the initial seeds are given by
RndSeed+my rank+1 at each ranks.NSplitSizeType : int-type (Positive integer, default value: 1)
Description : The number of processes of MPI parallelization.
NStoreType : int-type (0 or 1, default value: 1)
Description : The option of applying matrix-matrix product to calculate expected values \(\langle O_k O_l \rangle\) (0: off, 1: on). This speeds up calculation but increases the amount of memory usage from \(O(N_\text{p}^2)\) to \(O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})\), where \(N_\text{p}\) is the number of the variational parameters and \(N_\text{MCS}\) is the number of Monte Carlo sampling.
NSRCGType : int-type (0 or 1, default value: 0)
Description : The option of solving \(Sx=g\) in the SR method without constructing \(S\) matrix [NeuscammanUmrigarChan ]. (0: off, 1: on). This reduces the amount of memory usage from \(O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})\) to \(O(N_\text{p}) + O(N_\text{p}N_\text{MCS})\) when \(N_\text{p} > N_\text{MCS}\).
useDiagScaleType : int-type (0 or 1, default value: 0)
Description : The option of using the point Jacobi method (scaling by diagonal elements of \(S\) matrix) when solving the linear equation \(Sx=g\) in the SR method by CG method (0: off, 1: on,
NSRCGmust be 1).NSRCG=2is also accepted as a shortcut and is internally treated asNSRCG=1withuseDiagScale=1.NSRCGFallbackType : int-type (0 or 1, default value: 0)
Description : The option of retrying the other SR-CG solver when the selected solver does not converge or becomes numerically unstable (0: off, 1: on). Standard CG falls back to DiagScale-CG, and DiagScale-CG falls back to standard CG.
NSRCGAbortOnFailType : int-type (0 or 1, default value: 1)
Description : The option of aborting the calculation when SR-CG fails after the optional fallback (0: warn and continue with the approximate solution, 1: abort).
By default,
NSRCGFallback=0andNSRCGAbortOnFail=1. With these settings, a non-converged or numerically unstable SR-CG solve is treated as an input or numerical failure. IncreaseNVMCSample, adjust the SR-CG tolerance/iteration limit, or enableuseDiagScalewhen the overlap matrix is too noisy or ill-conditioned.useDiagScale=1selects the point-Jacobi preconditioned CG solver, which can improve convergence.RescaleSmatType : int-type (0 or 1, default value: 0)
Description : The option of rescaling Slater-related blocks in SR-CG before solving \(Sx=g\) (0: off, 1: on).
RescaleSmat=1requiresNSRCG=1(the rescaling is only applied along the SR-CG path). Typical settings for SR-CG inModParaare:NSRCG = 1 useDiagScale = 1 RescaleSmat = 1
NneuronGeneralType : int-type (default value: 0)
Description : The number of neurons \(N_{\rm General RBM}\) in the hidden layer of RBM.
LocSpin file (locspn.def)¶
This file determines sites with localized spins. An example of the file format is shown as follows.
================================
NlocalSpin 6
================================
========i_0LocSpn_1IteElc ======
================================
0 1
1 0
2 1
3 0
4 1
5 0
6 1
7 0
8 1
9 0
10 1
11 0
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of localized spins. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of localized spins.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ] \(<\)
Nsite).[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer for selecting an electron state whether localized spin or itinerant electron states (0: Itinerant electron state, 1: localized spin state with \(S=1/2\)).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of localized spins indicated by [ int03 ].
A program is terminated, when [ int02 ] is different from the total number of sites.
A program is terminated under the condition [ int02 ] \(<0\) or
Nsite\(\leq\) [ int02 ].
Trans file (trans.def)¶
The Hamiltonian for general one-body interactions
is added to the whole Hamiltonian by setting the parameters \(t_{ij\sigma_1\sigma2}\). An example of the file format is shown as follows.
========================
NTransfer 24
========================
========i_j_s_tijs======
========================
0 0 2 0 1.000000 0.000000
2 0 0 0 1.000000 0.000000
0 1 2 1 1.000000 0.000000
2 1 0 1 1.000000 0.000000
2 0 4 0 1.000000 0.000000
4 0 2 0 1.000000 0.000000
2 1 4 1 1.000000 0.000000
4 1 2 1 1.000000 0.000000
4 0 6 0 1.000000 0.000000
6 0 4 0 1.000000 0.000000
4 1 6 1 1.000000 0.000000
6 1 4 1 1.000000 0.000000
6 0 8 0 1.000000 0.000000
8 0 6 0 1.000000 0.000000
…
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3-5: Header
Lines 6-: [int02] [int03] [int04] [int05] [double01] [double02]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of transfer integrals. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of transfer integrals.
[ int02 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int04 ] \(<\)
Nsite).[ int03 ], [ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index,
0: up-spin,
1: down-spin.
[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for a real part of \(t_{ij\sigma_1\sigma_2}\).
[ double02 ]
Type : double-type (blank parameter not allowed)
Description : A value for an imaginary part of \(t_{ij\sigma_1\sigma_2}\).
Use rules¶
Headers cannot be omitted.
Blank line is not allowed.
A program is terminated, when [ int01 ] is different from the total number of transfer integrals defined in this file.
A program is terminated, when [ int02 ]-[ int05 ] are out of range from the defined values.
Since Hamiltonian must be Hermitian, the following relation must be satisfied, \(t_{ij\sigma_1\sigma_2}=t_{ji\sigma_2\sigma_1}^{\dagger}\).
InterAll file¶
The Hamiltonian for general two-body interactions
is added to the whole Hamiltonian by setting the parameters \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\). An example of file format is shown as follows.
======================
NInterAll 36
======================
========zInterAll=====
======================
0 0 0 1 1 1 1 0 0.50 0.0
0 1 0 0 1 0 1 1 0.50 0.0
0 0 0 0 1 0 1 0 0.25 0.0
0 0 0 0 1 1 1 1 -0.25 0.0
0 1 0 1 1 0 1 0 -0.25 0.0
0 1 0 1 1 1 1 1 0.25 0.0
2 0 2 1 3 1 3 0 0.50 0.0
2 1 2 0 3 0 3 1 0.50 0.0
2 0 2 0 3 0 3 0 0.25 0.0
2 0 2 0 3 1 3 1 -0.25 0.0
2 1 2 1 3 0 3 0 -0.25 0.0
2 1 2 1 3 1 3 1 0.25 0.0
4 0 4 1 5 1 5 0 0.50 0.0
4 1 4 0 5 0 5 1 0.50 0.0
4 0 4 0 5 0 5 0 0.25 0.0
4 0 4 0 5 1 5 1 -0.25 0.0
4 1 4 1 5 0 5 0 -0.25 0.0
4 1 4 1 5 1 5 1 0.25 0.0
...
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09] [double01] [double02]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of generalized two body interactions. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of generalized two body interactions.
[ int02 ], [ int04 ], [ int06 ], [ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 \(], [\) int04 ], [ int06 ], [ int08 ] \(<\)
Nsite).[ int03 ], [ int05 ], [ int07 ], [ int09 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index,
0: up-spin,
1: down-spin.
[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for a real part of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\).
[ double02 ]
Type : double-type (blank parameter not allowed)
Description : A value for an imaginary part of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\).
Use rules¶
Headers cannot be omitted.
Since Hamiltonian must be Hermitian, the following relation must be satisfied, \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}=I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}^{\dagger}\).
A program is terminated, when [ int01 ] is different from the total number of generalized two body interactions defined in this file.
A program is terminated, when [ int02 ]-[ int09 ] are out of range from the defined values.
CoulombIntra file (coulombintra.def)¶
The Hamiltonian for the coulombintra interactions
is added to the whole Hamiltonian by setting \(U_i\). An example of the file format is shown as follows.
======================
NCoulombIntra 6
======================
========i_0LocSpn_1IteElc ======
======================
0 4.000000
1 4.000000
2 4.000000
3 4.000000
4 4.000000
5 4.000000
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [double01]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of on-site interactions. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of on-site interactions.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ] \(<\)
Nsite).[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for \(U_i\).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of on-site interactions defined in this file.
A program is terminated, when [ int02 ] is out of range from the defined values.
CoulombInter file (coulombinter.def)¶
The Hamiltonian for the coulombinter interactions
is added to the whole Hamiltonian by setting \(V_{ij}\). An example of the file format is shown as follows.
======================
NCoulombInter 6
======================
========CoulombInter ======
======================
0 1 1.0000
1 2 1.0000
2 3 1.0000
3 4 1.0000
4 5 1.0000
5 0 1.0000
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [double01]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of off-site interactions. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of off-site interactions.
[ int02 ], [ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int03 ] \(<\)
Nsite).[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for \(V_{ij}\).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of off-site interactions defined in this file.
A program is terminated, when either [ int02 ] or [ int03 ] are out of range from the defined values.
Hund file (hund.def)¶
The Hamiltonian for Hund couplings
is added to the whole Hamiltonian by setting the parameters \(J_{ij}^{\rm Hund}\). An example of the file format is shown as follows.
======================
NHund 6
======================
========Hund ======
======================
0 1 -0.250000
1 2 -0.250000
2 3 -0.250000
3 4 -0.250000
4 5 -0.250000
5 0 -0.250000
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [double01]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of Hund couplings. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of Hund couplings.
[ int02 ], [ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int03 ] \(<\)
Nsite).[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for \(J_{ij}^{\rm Hund}\).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of Hund couplings defined in this file.
A program is terminated, when either [ int02 ] or [ int03 ] are out of range from the defined values.
PairHop file¶
The Hamiltonian for PairHop couplings
is added to the whole Hamiltonian by setting the parameters \(J_{ij}^{\rm Pair}\). An example of the file format is shown as follows.
======================
NPairhop 6
======================
========Pairhop ======
======================
0 1 0.50000
1 2 0.50000
2 3 0.50000
3 4 0.50000
4 5 0.50000
5 0 0.50000
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [double01]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of PairHop couplings. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of PairHop couplings.
[ int02 ], [ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int03 ] \(<\)
Nsite).[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for \(J_{ij}^{\rm Pair}\).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of PairHop couplings defined in this file.
A program is terminated, when either [ int02 ] or [ int03 ] are out of range from the defined values.
Exchange file (exchange.def)¶
The Hamiltonian for exchange couplings
is added to the whole Hamiltonian by setting \(J_{ij}^{\rm Ex}\). Note that, for spin systems, the definition of the Exchange is different from that in HPhi. An example of the file format is shown as follows.
======================
NExchange 6
======================
========Exchange ======
======================
0 1 0.50000
1 2 0.50000
2 3 0.50000
3 4 0.50000
4 5 0.50000
5 0 0.50000
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3-5: Header
Lines 6-: [int02] [int03] [double01]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of Exchange couplings. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of Exchange couplings.
[ int02 ], [ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int03 ] \(<\)
Nsite).[ double01 ]
Type : double-type (blank parameter not allowed)
Description : A value for \(J_{ij}^{\rm Ex}\).
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of Exchange couplings defined in this file.
A program is terminated, when either [ int02 ] or [ int03 ] are out of range from the defined values.
Gutzwiller file (gutzwiller.def)¶
This file sets the calculation conditions of Gutzwiller factors
A site number \(i\) and the variational parameters \(g_i\) are specified. An example of the file format is shown as follows.
======================
NGutzwillerIdx 2
ComplexType 0
======================
======================
0 0
1 0
2 0
3 1
(continue...)
12 1
13 0
14 0
15 0
0 1
1 0
File format¶
In the following, we define the whole number of sites as \(N_s\) and variational parameters as \(N_g\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s\)): [int03] [int04]
Lines (6+ \(N_s\)) - (5+ \(N_s\) + \(N_g\)): [int05] [int06]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters \(g_i\). You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters \(g_i\).
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters \(g_i\). You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters \(g_i\) (0: double, 1: complex).
[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ] \(<\)
Nsite).[ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters \(g_i\) (0 \(\leq\) [ int04 ] \(<\) [ int01]).
[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int05] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when components of variational parameters are double counted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int06 ] are out of range from the defined values.
Jastrow file (jastrow.def)¶
This file sets the calculation conditions of Jastrow factors
Site numbers \(i\) \(j\), and the variational parameters \(v_{ij}\) are specified. An example of the file format is shown as follows.
======================
NJastrowIdx 5
ComplexType 0
======================
======================
0 1 0
0 2 1
0 3 0
(continue...)
0 1
1 1
2 1
3 1
4 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_j\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s\times (N_s-1))\): [int03] [int04] [int05]
Lines (6+ \(N_s\times (N_s-1)\)) - (5+ \(N_s\times (N_s-1)\) + \(N_j\)): [int06] [int07]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters \(v_{ij}\). You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters \(v_{ij}\).
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters \(v_{ij}\). You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters \(v_{ij}\) (0: double, 1: complex).
[ int03 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ] \(<\)
Nsite).[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters \(v_{ij}\) (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int06] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int07 ] are out of range from the defined values.
Spin Jastrow file (spinjastrow.def)¶
This file sets the calculation conditions of spin Jastrow factors
Site numbers \(i\) and \(j\), and the variational parameters \(v^s_{ij}\) are specified. An example of the file format is shown as follows.
======================
NSpinJastrowIdx 4
ComplexType 0
=====================
=====================
0 1 0
0 2 1
0 3 2
1 0 0
(continue...)
0 1
1 1
2 1
3 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{sj}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s\times (N_s-1)\)): [int03] [int04] [int05]
Lines (6+ \(N_s\times (N_s-1)\)) - (5+ \(N_s\times (N_s-1)\) + \(N_{sj}\)): [int06] [int07]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters \(v^s_{ij}\). You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters \(v^s_{ij}\).
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters \(v^s_{ij}\). You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters \(v^s_{ij}\) (0: double, 1: complex).
[ int03 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ] \(<\)
Nsite).[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters \(v^s_{ij}\) (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int06] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int07 ] are out of range from the defined values.
A program is terminated, when [ int03 ] and [ int04 ] indicate the same site.
Both directed pairs \((i,j)\) and \((j,i)\) must be specified for each pair of sites, and they must have the same parameter index.
DH2 file¶
This file sets the calculation conditions of 2-site doublon-holon correlation factors
A site number \(i\), the two sites around \(i\) site and the variational parameters \(\alpha_{2nt}^{d(h)}\) which have \(t\) kinds at each sites are specified. The details of the parameters \(\alpha_{2nt}^{d(h)}\) and the operator \(\xi_{i2nt}^{d(h)}\) are shown in ref. [Tahara2008 ]. An example of the file format is shown as follows.
====================================
NDoublonHolon2siteIdx 2
ComplexType 0
====================================
====================================
0 5 15 0
0 13 7 1
(continue...)
15 8 2 1
0 1
(continue...)
11 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{\rm dh2}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s\times N_{\rm dh2})\): [int03] [int04] [int05] [int06]
Lines (6+ \(N_s\times N_{\rm dh2}\)) - (5+ \((N_s+6) \times N_{\rm dh2})\): [int07] [int08]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters. You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters (0: double, 1: complex).
[ int03 ], [ int04 ], [ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ], [ int05 ] \(<\)
Nsite).[ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters. The value is \((2n+s)\times\) [int01]:math:+t, where \(n\), \(s\) and \(t\) are given by the following relation:
\(n\): The number of doublon (holon) around the center site (0, 1, 2),
\(s\): When the center is doublon (holon), s=0 (1),
\(t\): The kind of variational parameters (0, \(\cdots\) [int1]-1).
[ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int07] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int08 ] are out of range from the defined values.
DH4 file¶
This file sets the calculation conditions of 4-site doublon-holon correlation factors
A site number \(i\), the four sites around \(i\) site and the variational parameters \(\alpha_{4nt}^{d(h)}\) which have \(t\) kinds at each sites are specified. The details of the parameters \(\alpha_{4nt}^{d(h)}\) and the operator \(\xi_{i4nt}^{d(h)}\) are shown in ref. [Tahara2008 ]. An example of the file format is shown as follows.
====================================
NDoublonHolon4siteIdx 1
ComplexType 0
====================================
====================================
0 1 3 4 12 0
1 2 0 5 13 0
(continue...)
15 12 14 3 11 0
0 1
(continue...)
9 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{\rm dh4}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s\times N_{\rm dh4}\)): [int03] [int04] [int05] [int06] [int07] [int08]
Lines (6+ \(N_s\times N_{\rm dh4}\)) - (5+ \((N_s+10) \times N_{\rm dh4}\)): [int09] [int10]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters. You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters (0: double, 1: complex).
[ int03 ], [ int04 ], [ int05 ], [ int06 ], [ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 \(], \cdots, [\) int07 ] \(<\)
Nsite).[ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int08 ] \(<\) [ int01]).
[ int09 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters. The value is \((2n+s)\times\) [int01]:math:+t, where \(n\), \(s\) and \(t\) are given by the following relation:
\(n\): The number of doublon (holon) around the center site (0, 1, 2, 3, 4),
\(s\): When the center is doublon (holon), s=0 (1),
\(t\): The kind of variational parameters (0, \(\cdots\) [int1]-1).
[ int10 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int09] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when components of variational parameters are double counted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int10 ] are out of range from the defined values.
GeneralRBM_PhysLayer file¶
In the general RBM correlation factors,
this file sets the calculation conditions of \(\exp \left[ \sum_i a_{i\sigma} n_{i\sigma} \right] ` . A site index :math:`i\), a spin index \(\sigma\) and the variational parameters \(a_{i \sigma}\) are specified. An example of the file format is shown as follows.
--------------------
NRBM_PhysLayerIdx 1
ComplexType 1
i s RBM_PhysLayer_Idx
--------------------
0 0 0
0 1 0
1 0 0
1 1 0
(continue...)
0 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{v}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(2N_s\)): [int03] [int04] [int05]
Lines (6+ \(2N_s\) ) - (5+ \(2N_s\) + \(N_v\)): [int06] [int07]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters \(a_{i\sigma}\). You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters \(a_{i\sigma}\).
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters \(a_{i\sigma}\). You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters \(a_{i\sigma}\) (0: double, 1: complex).
[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ] \(<\)
Nsite).[ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index ([int04] = 0 or 1).
[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters \(v_{ij}\) (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int06] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
This function is a beta version. Please use it carefully. The file format and the implementation may be changed in the future release.
This function is available only for the VMC calculation with
ComplexType=1andOrbital. This function is not available for the Power Lanczos calculations.Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int07 ] are out of range from the defined values.
Orbital/OrbitalAntiParallel file (orbitalidx.def)¶
This file sets the calculation conditions of pair orbitals
Site numbers \(i, j\) and the variational parameters \(f_{ij}\) are indicated. An example of the file format is shown as follows.
====================================
NOrbitalIdx 64
ComplexType 0
====================================
====================================
0 0 0
0 1 1
0 2 2
0 3 3
(continue...)
15 9 62
15 10 63
0 1
1 1
(continue...)
62 1
63 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{\rm o}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s^2\)): [int03] [int04] [int05] [int06]
Lines (6+ \(N_s^2\) )- (5+ \(N_s^2+N_{\rm o}\)): [int06] [int07]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters. You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters (0: double, 1: complex).
[ int03 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ] \(<\)
Nsite).[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type
Description : When the mode of the anti-periodic condition turns on (the mode turns on when the value of
NMPTransinModParafile is negative), the sign of \(f_{ij}\) is specified by setting [ int06 \(]=\pm1\). This term can be omitted when the mode of the anti-periodic condition is off.[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int06] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int09 ] are out of range from the defined values.
OrbitalParallel file¶
This file sets the calculation conditions of pair orbitals
Site numbers \(i, j\), the spin index \(\sigma\) and the variational parameters \(f_{i\sigma j\sigma}\) are indicated. The indexes of \(f_{i\sigma j\sigma}\) must satisfy the condition \(i < j `, where :math:\)sigma = 0` or \(1\) and process will terminate when the condition is broken. An example of the file format is shown as follows.
====================================
NOrbitalIdx 120
ComplexType 0
====================================
====================================
0 1 0
0 2 1
0 3 2
(continue...)
15 13 118
15 14 119
0 1
1 1
(continue...)
118 1
119 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{\rm o}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_s*(N_s-1)/2\)): [int03] [int04] [int05] [int06]
Lines (6+ \(N_s*(N_s-1)/2\) )- (5+ \(N_s*(N_s-1)/2+N_{\rm o}\)): [int06] [int07]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters. You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters (0: double, 1: complex).
[ int03 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ] \(<\)
Nsite).[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int05 ] \(<\) [ int01]).
[ int06 ]
Type : int-type
Description : When the mode of the anti-periodic condition turns on (the mode turns on when the value of
NMPTransinModParafile is negative), the sign of \(f_{ij}\) is specified by setting [ int06 \(]=\pm1\). This term can be omitted when the mode of the anti-periodic condition is off.[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int06 ] \(<\) [ int01]).
[ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int06] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int09 ] are out of range from the defined values.
OrbitalGeneral file¶
This file sets the calculation conditions of pair orbitals
Site numbers \(i, j\), spin indexes \(\sigma_1, \sigma_2\) and the variational parameters \(f_{i\sigma_1j\sigma_2}\) are indicated. The indexes of \(f_{i\sigma_1j\sigma_2}\) must satisfy the condition \(i+\sigma_1 N_s < j+\sigma_2 N_s\), where \(\sigma_i = 0\) or \(1\) and process will terminate when the condition is broken. An example of the file format is shown as follows.
12.5cm
====================================
NOrbitalIdx 255
ComplexType 0
====================================
====================================
0 0 0 1 0
0 0 1 1 1
(continue...)
14 0 15 1 253
15 0 15 1 254
0 1
1 1
(continue...)
253 1
254 1
File format¶
In the following, we define the total number of sites as \(N_s\) and variational parameters as \(N_{\rm o}\), respectively. A total number of variational parameters \(N_p\) is given by \(N_s^2\), \(2 N_s^2 -N_s\) in \(Sz\) conserved and \(S_z\) unconserved system, respectively.
Line 1: Header
Line 2: [string01] [int01]
Line 3: [string02] [int02]
Lines 4 - 5: Header
Lines 6 - (5+ \(N_p\)): [int03] [int04] [int05] [int06] [int07] [int08]
Lines (6+ \(N_p\)) - (5+ \(N_p+N_{\rm o}\)): [int09] [int10]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ string02 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for indicating the double or complex type of variational parameters. You can freely give a name of the keyword.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer indicates the double or complex type of variational parameters (0: double, 1: complex).
[ int03 ], [ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ], [ int04 ] \(<\)
Nsite).[ int04 ], [ int06 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index (\(0:\uparrow\) spin, \(1:\downarrow\) spin).
[ int07 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int07 ] \(<\) [ int01]).
[ int08 ]
Type : int-type
Description : When the mode of the anti-periodic condition turns on (the mode turns on when the value of
NMPTransinModParafile is negative), the sign of \(f_{i\sigma_1j\sigma_2}\) is specified by setting [ int08 \(]=\pm1\). This term can be omitted when the mode of the anti-periodic condition is off.[ int09 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of variational parameters (0 \(\leq\) [ int09 ] \(<\) [ int01]).
[ int10 ]
Type : int-type (blank parameter not allowed)
Description : An integer to select the target of variational parameters indicated at [int09] to be optimized or not (0: not optimize, 1: optimize).
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
A program is terminated, when [ int02 ] - [ int10 ] are out of range from the defined values.
TransSym file (qptransidx.def)¶
This file sets the weight and corresponding site numbers of momentum projection \({\cal L}_K=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R}\) and lattice translational projection \({\cal L}_P=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha}\). The patterns of projection are indicated by \((\alpha, {\boldsymbol R})\). We note that the weight must be equal to \(1.0\) when the projection is not done. An example of the file format is shown as follows.
12.5cm
====================================
NQPTrans 4
====================================
== TrIdx_TrWeight_and_TrIdx_i_xi ==
====================================
0 1.000000 0.000000
1 1.000000 0.000000
2 1.000000 0.000000
3 1.000000 0.000000
0 0 0
(continue...)
3 12 1
3 13 2
File format¶
In the following, we define the total number of sites as \(N_s\) and projection patterns as \(N_{\rm TS}\), respectively.
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 - (5+ \(N_{\rm TS})\): [int02] [double01] [double02]
Lines (6+ \(N_{\rm TS}\)) - (5+ \((N_s+1) \times N_{\rm TS}\)): [int03] [int04] [int05] [int06]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of projection patterns. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of projection patterns.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the projection pattern \((\alpha, {\boldsymbol R})\) (0 \(\leq\) [ int02 ] \(<\) [ int01]).
[ double01 ]
Type : double-type (blank parameter not allowed)
Description : The weight Real part of \(p_{\alpha}\cos ({\boldsymbol K}\cdot {\boldsymbol R})\) of the projection pattern \((\alpha, {\boldsymbol R})\).
[ double02 ]
Type : double-type (blank parameter not allowed)
Description : The weight Imaginary part of \(p_{\alpha}\cos ({\boldsymbol K}\cdot {\boldsymbol R})\) of the projection pattern \((\alpha, {\boldsymbol R})\).
[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving kinds of the projection pattern \((\alpha, {\boldsymbol R})\) (0 \(\leq\) [ int03 ] \(<\) [ int01]).
[ int04 ], [ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int04 ], [ int05 ] \(<\)
Nsite). The site number [ int05 ] is given by applying the translation and point group transformation indicated by [ int03 ] to the site [ int04 ].[ int06 ]
Type : int-type
Description : When the mode of the anti-periodic condition turns on (the mode turns on when the value of
NMPTransinModParafile is negative), the sign of the translational operator is specified by setting [ int06 ] \(=\pm1\). This term can be omitted when the mode of the anti-periodic condition is off.
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of projection patterns defined in this file.
A program is terminated, when [ int02 ] - [ int06 ] are out of range from the defined values.
Files to set initial values of variational parameters¶
This file sets the initial values of variational parameters. The kinds
of variational parameters are specified by setting the following
keywords in List file (namelist.def):
InGutzwiller, InJastrow, InSpinJastrow, InDH2, InDH4, InGeneralRBM_PhysLayer, InGeneralRBM_HiddenLayer, InGeneralRBM_PhysHidden, InOrbital,
InOrbitalAntiParallel, InOrbitalParallel,
InOrbitalGeneral.
The file format is common and an example of the InJastrow file is
shown as follows.
For InSpinJastrow, set the second line to the number of spin
Jastrow parameters, for example NSpinJastrowIdx.
======================
NJastrowIdx 28
======================
== i_j_JastrowIdx ===
======================
0 -8.909963465082626488e-02 0.000000000000000000e+00
1 5.521681211878626955e-02 0.000000000000000000e+00
(continue...)
27 -9.017586139930480749e-02 0.000000000000000000e+00
File format¶
In the following, we define the total number of variational parameters as \(N_v\).
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 - (5+ \(N_v\)): [int03] [double01] [double02]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of variational parameters. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of variational parameters.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer setting kinds of variational parameters (0 \(\leq\) [ int02 ] \(<\) [ int01]).
[ double01 ]
Type : double-type (blank parameter not allowed)
Description : The real part of the variational parameter indicated by [int01].
[ double02 ]
Type : double-type
Description : The imaginary part of the variational parameter indicated by [int01].
User rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of variational parameters defined in this file.
OneBodyG file (greenone.def)¶
This file determines the target components to calculate and output one-body Green’s function \(\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\rangle\). An example of file format is shown as follows.
===============================
NCisAjs 24
===============================
======== Green functions ======
===============================
0 0 0 0
0 1 0 1
1 0 1 0
1 1 1 1
2 0 2 0
2 1 2 1
3 0 3 0
3 1 3 1
4 0 4 0
4 1 4 1
5 0 5 0
5 1 5 1
6 0 6 0
6 1 6 1
7 0 7 0
7 1 7 1
8 0 8 0
8 1 8 1
9 0 9 0
9 1 9 1
10 0 10 0
10 1 10 1
11 0 11 0
11 1 11 1
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [int04] [int05]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of one-body Green’s functions. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of one-body Green’s functions.
[ int02 ], [ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int04 ] \(<\)
Nsite).[ int03 ], [ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index,
0: up-spin,
1: down-spin.
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of one-body Green’s functions defined in this file.
A program is terminated, when [ int02 ]-[ int05 ] are out of range from the defined values.
TwoBodyG file (greentwo.def)¶
This file determines the target components to calculate and output two-body Green’s function \(\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\rangle\). For Spin, the condition \(i=j\) and \(k=l\) must be satisfied. An example of file format is shown as follows.
=============================================
NCisAjsCktAltDC 576
=============================================
======== Green functions for Sq AND Nq ======
=============================================
0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 1
0 0 0 0 1 0 1 0
0 0 0 0 1 1 1 1
0 0 0 0 2 0 2 0
0 0 0 0 2 1 2 1
0 0 0 0 3 0 3 0
0 0 0 0 3 1 3 1
0 0 0 0 4 0 4 0
0 0 0 0 4 1 4 1
0 0 0 0 5 0 5 0
0 0 0 0 5 1 5 1
0 0 0 0 6 0 6 0
0 0 0 0 6 1 6 1
0 0 0 0 7 0 7 0
0 0 0 0 7 1 7 1
0 0 0 0 8 0 8 0
0 0 0 0 8 1 8 1
0 0 0 0 9 0 9 0
0 0 0 0 9 1 9 1
0 0 0 0 10 0 10 0
0 0 0 0 10 1 10 1
0 0 0 0 11 0 11 0
0 0 0 0 11 1 11 1
0 1 0 1 0 0 0 0
...
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [int04] [int05] [int06] [int07] [int08] [int09]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of two-body Green’s functions. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving total number of two-body Green’s functions.
[ int02 ], [ int04 ], [ int06 ], [ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int02 ], [ int04 ], [ int06 ], [ int08 ] \(<\)
Nsite).[ int03 ], [ int05 ], [ int07 ], [ int09 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index,0: up-spin,1: down-spin.
Use rules¶
Headers cannot be omitted.
A program is terminated, when [ int01 ] is different from the total number of two-body Green’s functions defined in this file.
A program is terminated, when [ int02 ]-[ int09 ] are out of range from the defined values.
Twist file (twist.def)¶
This file sets the target components to calculate and output the Twist operator \(P^{(\alpha)} = \langle \exp ( i 2\pi \sum_{i\sigma} \sum_{\mu=x,y,z} c^{(\alpha)\mu }_{i\sigma } \mu_{i} n_{i\sigma} ) \rangle\). Position operator \(\mu_i\) is defined in Lattice definition file (lattice.def). An example of file format is shown as follows.
--------------------
NTwist 2
--------------------
idx_site_s_x_y_z
--------------------
0 0 0 0.0 0.0 0.0
0 1 0 0.0 0.0 0.0
0 2 0 0.0 0.0 0.0
0 3 0 0.0 0.0 0.0
0 4 0 0.0 0.0 0.0
0 5 0 0.0 0.0 0.0
0 0 1 0.3333333333 0.0 0.0
0 1 1 0.3333333333 0.0 0.0
0 2 1 0.3333333333 0.0 0.0
0 3 1 0.3333333333 0.0 0.0
0 4 1 0.3333333333 0.0 0.0
0 5 1 0.3333333333 0.0 0.0
1 0 0 0.3333333333 0.0 0.0
1 1 0 0.3333333333 0.0 0.0
…
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3 - 5: Header
Lines 6 -: [int02] [int03] [int04] [double01] [double02] [double03]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword for total number of Twist operators. You can freely give a name of the keyword.
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the total number of Twist operators.
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a Twist operator index \(\alpha\). You can specify it as an integer from 0 to [ int01 ]-1.
[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int03 ] \(<\)
Nsite).[ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a spin index, 0: up-spin, 1: down-spin.
[ double01 ], [ double02 ], [ double03 ]
Type : double-type (blank parameter not allowed)
Description : \(c^{(\alpha)\mu}_{i\sigma}\) for \(\mu = x, y, z\), \(c^{(\alpha)\mu}_{i\sigma}\). You need to specify the \(x\) direction component as [ double01 ], the \(y\) direction component as [ double02 ], and the \(z\) direction component as [ double03 ].
Use rules¶
Headers cannot be omitted.
All the combinations of sites and spins must be specified to designate each Twist operator.
Lattice file (lattice.def)¶
This file defines the position operator \(\mu_i\) corresponding to site number \(i\) and the orbital number in the unit cell. An example of file format is shown as follows.
--------------------
NLattice 4 4 4 2
--------------------
i_x_y_z_orb
--------------------
0 0 0 0 0
1 0 0 0 1
2 1 0 0 0
3 1 0 0 1
4 2 0 0 0
5 2 0 0 1
…
File format¶
Line 1: Header
Line 2: [string01] [int01] [int02] [int03] [int04]
Lines 3 - 5: Header
Lines 6 -: [int05] [int06] [int07] [int08] [int09]
Parameters¶
[ string01 ]
Type : string-type (blank parameter not allowed)
Description : A keyword name (optional).
[ int01 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the maximum value in the \(x\) direction for the position operator \(\mu\).
[ int02 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the maximum value in the \(y\) direction for the position operator \(\mu\).
[ int03 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the maximum value in the \(z\) direction for the position operator \(\mu\).
[ int04 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the number of orbitals in the unit cell.
[ int05 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving a site index (0 \(\leq\) [ int05 ] \(<\)
Nsite).[ int06 ], [ int07 ], [ int08 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the position operator \(\mu_i\) for site number [ int05 ] in each coordinate direction \(\mu = x, y, z\). You can specify the \(x, y, z\) direction components as 0 or greater and less than [ int01 ], [ int02 ], [ int03 ].
[ int09 ]
Type : int-type (blank parameter not allowed)
Description : An integer giving the orbital index in the unit cell corresponding to site number [ int05 ]. You can specify it as an integer from 0 to [ int04 ]-1.
Usage rules¶
The rules for using this file are as follows:
Headers cannot be omitted.
All the site indices must be specified.
[int01] * [int02] * [int03] * [int04](i.e.Nx * Ny * Nz * Norb) must equalNsite.Each site index must appear exactly once. Duplicate or missing indices are rejected as input errors.
