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.

1. 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.

2. 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.

3. Hamiltonian:

   Hamiltonian for mVMC is denoted by

   \[\begin{split}\begin{aligned} {\cal H}&={\cal H}_T+{\cal H}_U+{\cal H}_V+{\cal H}_H+{\cal H}_E+{\cal H}_P+{\cal H}_I,\\ {\cal H}_T&=-\sum_{i, j}\sum_{\sigma_1, \sigma2}t_{ij\sigma_1\sigma_2} c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\\ {\cal H}_U&=\sum_{i} U_i n_ {i \uparrow}n_{i \downarrow},\\ {\cal H}_V&=\sum_{i,j} V_{ij}n_ {i}n_{j},\\ {\cal H}_H&=-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow}),\\ {\cal H}_E&=\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow}+c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}),\\ {\cal H}_P&=\sum_{i,j}J_{ij}^{\rm Pair} c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow},\\ {\cal H}_I&=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}, \end{aligned}\end{split}\]

   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 \({\cal H}_I\).

4. 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

   \[\begin{split}\begin{aligned} |\psi \rangle &= {\cal P}_G{\cal P}_J{\cal P}_{d-h}^{(2)}{\cal P}_{d-h}^{(4)}{\cal L}^S{\cal L}^K{\cal L}^P |\phi_{\rm pair} \rangle,\\ {\cal P}_G&=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right],\\ {\cal P}_J&=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right],\\ {\cal P}_{d-h}^{(2)}&= \exp \left[ \sum_t \sum_{n=0}^2 (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right],\\ {\cal P}_{d-h}^{(4)}&= \exp \left[ \sum_t \sum_{n=0}^4 (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right],\\ {\cal L}_S&=\frac{2S+1}{8 \pi^2}\int d\Omega P_s(\cos \beta) \hat{R}(\Omega),\\ {\cal L}_K&=\frac{1}{N_s}\sum_{{\boldsymbol R}}e^{i {\boldsymbol K} \cdot{\boldsymbol R} } \hat{T}_{\boldsymbol R},\\ {\cal L}_P&=\sum_{\alpha}p_{\alpha} \hat{G}_{\alpha},\end{aligned}\end{split}\]

   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. 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.

   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.

   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 \({\cal L}_P\).

5. 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 \({\cal P}_J\).

   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 \({\cal P}_{d-h}^{(4)}\).

   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 \(|\phi_{\rm pair} \rangle\).

6. 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.

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.
DH2	2-site doublon-holon correlation factors.
DH4	4-site doublon-holon correlation factors.
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.
InDH2	Initial values of 2-site doublon-holon correlation factors.
InDH4	Initial values of 4-site doublon-holon correlation factors.
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 \(\langle c_{i\sigma}^{\dagger}c_{j\sigma}c_{k\tau}^{\dagger}c_{l\tau}\rangle\)

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

• NVMCCalMode

  Type : int-type (default value: 0)

  Description : [0] Optimization of variational parameters, [1] Calculation of one body and two body Green’s functions.

• NLanczosMode

  Type : 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).

• NDataIdxStart

  Type : int-type (default value: 0)

  Description : An integer for numbering of output files. For NVMCCalMode = 0 , NDataIdxStart is added at the end of the output files. For NVMCCalMode = 1, the files are outputted with the number from NDataIdxStart to NDataIdxStart + NDataQtySmp-1.

• NDataQtySmp

  Type : int-type (default value: 1)

  Description : The set number for outputted files (only used for NVMCCalMode = 1).

• Nsite

  Type : int-type (Positive integer)

  Description : The number of sites.

• Nelectron

  Type : int-type (Positive integer)

  Description : The number of electron pairs (the electron number is given by 2 Nelectron).

• Ncond

  Type : int-type (greater than 0)

  Description : The number of conduction electrons.

• 2Sz

  Type : int-type

  Description : The value of \(2S_z\). Since the electrons form pair, \(2S_z\) must be even number.

• NSPGaussLeg

  Type : 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.

• NSPStot

  Type : int-type ( greater than 0, default value: 0)

  Description : The spin quantum-number.

• NMPTrans

  Type : 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 NMPTrans with the specified weight indicated in TransSym file. In the case of not applying the projection, this value must be equal to 1.

• NSROptItrStep

  Type : int-type (Positive integer, default value: 1000)

  Description : The whole step number to optimize variational parameters by SR method. Only used for NVMCCalMode =0.

• NSROptItrSmp

  Type : int-type (Positive integer, default value: NSROptItrStep/10)

  Description : In the NSROptItrStep step, the average values of the each variational parameters at the NSROptItrStep step are adopted as the optimized values. Only used for NVMCCalMode =0.

• DSROptRedCut

  Type : 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 ].

• DSROptStaDel

  Type : 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 ].

• DSROptStepDt

  Type : double-type

  Description : The time step using in the SR method.

• NSROptCGMaxIter

  Type : 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.

• DSROptCGTol

  Type : 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.

• NVMCWarmUp

  Type : int-type (Positive integer, default value: 10)

  Description : Idling number for the Malkov chain Montecarlo Methods.

• NVMCInterval

  Type : int-type (Positive integer, default value: 1)

  Description : The interval step between samples. The local update will be performed Nsite × NVMCInterval times.

• NVMCSample

  Type : int-type (Positive integer, default value: 1000)

  Description : The sample numbers to calculate the expected values.

• NExUpdatePath

  Type : int-type (Positive integer)

  Description : The option for local update about exchange terms. 0: not update, 1: update for electron system. For Spin system, the value must be 2.

• RndSeed

  Type : 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.

• NSplitSize

  Type : int-type (Positive integer, default value: 1)

  Description : The number of processes of MPI parallelization.

• NStore

  Type : 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.

• NSRCG

  Type : 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 \(N_\text{p} > N_\text{MCS}\).

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

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

\[\begin{aligned} {\cal H}_{T} =-\sum_{ij\sigma_1\sigma2} t_{ij\sigma_1\sigma2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2},\end{aligned}\]

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

\[\begin{aligned} {\cal H}_I =\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4} c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}. \end{aligned}\]

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

\[{\cal H}_U =\sum_{i}U_i n_ {i \uparrow}n_{i \downarrow}\]

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

\[{\cal H}_V = \sum_{i,j}V_{ij} n_ {i} n_{j}\]

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

\[{\cal H}_H =-\sum_{i,j}J_{ij}^{\rm Hund} (n_{i\uparrow}n_{j\uparrow}+n_{i\downarrow}n_{j\downarrow})\]

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

\[{\cal H}_P=\sum_{i,j}J_{ij}^{\rm Pair} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{i \downarrow}^{\dagger}c_{j \downarrow} +c_{j \downarrow}^{\dagger}c_{i \downarrow}c_ {j \uparrow}^{\dagger}c_{i\uparrow})\]

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

\[{\cal H}_E =\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow} +c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow})\]

is added to the whole Hamiltonian by setting \(J_{ij}^{\rm Ex}\). 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

\[{\cal P}_G=\exp\left[ \sum_i g_i n_{i\uparrow} n_{i\downarrow} \right].\]

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

\[{\cal P}_J=\exp\left[\frac{1}{2} \sum_{i\neq j} v_{ij} (n_i-1)(n_j-1)\right]\]

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.

DH2 file

This file sets the calculation conditions of 2-site doublon-holon correlation factors

\[{\cal P}_{d-h}^{(2)}= \exp \left[ \sum_t \sum_{n=0}^2 (\alpha_{2nt}^d \sum_{i}\xi_{i2nt}^d+\alpha_{2nt}^h \sum_{i}\xi_{i2nt}^h)\right].\]

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

\[{\cal P}_{d-h}^{(4)}= \exp \left[ \sum_t \sum_{n=0}^4 (\alpha_{4nt}^d \sum_{i}\xi_{i4nt}^d+\alpha_{4nt}^h \sum_{i}\xi_{i4nt}^h)\right]\]

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.

Orbital/OrbitalAntiParallel file (orbitalidx.def)

This file sets the calculation conditions of pair orbitals

\[|\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} f_{ij}c_{i\uparrow}^{\dagger}c_{j\downarrow}^{\dagger} \right]^{N/2}|0 \rangle.\]

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 NMPTrans in ModPara file 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

\[|\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma} f_{i\sigma j\sigma}c_{i\sigma}^{\dagger}c_{j\sigma}^{\dagger} \right]^{N/2}|0 \rangle.\]

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 NMPTrans in ModPara file 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

\[|\phi_{\rm pair} \rangle = \left[\sum_{i, j=1}^{N_s} \sum_{\sigma_1, \sigma_2} f_{i\sigma_1j\sigma_2}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}^{\dagger} \right]^{N/2}|0 \rangle.\]

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 NMPTrans in ModPara file 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
   1  1.000000
   2  1.000000
   3  1.000000
   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]
• 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 \(p_{\alpha}\cos ({\boldsymbol K}\cdot {\boldsymbol R})\) 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 NMPTrans in ModPara file 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, InDH2, InDH4, InOrbital, InOrbitalAntiParallel, InOrbitalParallel, InOrbitalGeneral. The file format is common and an example of the InJastrow file is shown as follows.

======================
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.