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

    H=HT+HU+HV+HH+HE+HP+HI,HT=i,jσ1,σ2tijσ1σ2ciσ1cjσ2,HU=iUinini,HV=i,jVijninj,HH=i,jJijHund(ninj+ninj),HE=i,jJijEx(cicjcjci+cicjcjci),HP=i,jJijPaircicjcicj,HI=i,j,k,lσ1,σ2,σ3,σ4Iijklσ1σ2σ3σ4ciσ1cjσ2ckσ3clσ4,

    as the format of interactions for electron system. Here, we define the charge density operator with spin σ at site i as niσ=ciσciσ and the total charge density operator at site i as ni=ni+ni. Each parameters are specified by the following files, respectively;

    Trans (trans.def): tijσ1σ2 in HT,

    CoulombIntra (coulombintra.def): Ui in HU,

    CoulombInter (coulombinter.def): Vij in HV,

    Hund (hund.def): JijHund in HH,

    Exchange (exchange.def): JijEx in HE,

    PairHop: JijPair in HP,

    InterAll: Iijklσ1σ2σ3σ4 in HI.

  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

    |ψ=NGeneralRBMPGPJPdh(2)Pdh(4)LSLKLP|ϕpair,PG=exp[iginini],PJ=exp[12ijvij(ni1)(nj1)],Pdh(2)=exp[tn=02(α2ntdiξi2ntd+α2nthiξi2nth)],Pdh(4)=exp[tn=04(α4ntdiξi4ntd+α4nthiξi4nth)],NGeneralRBM=exp[iaiσniσ]kNhcosh[bk+iσWiσkniσ],LS=2S+18π2dΩPs(cosβ)R^(Ω),LK=1NsReiKRT^R,LP=αpαG^α,

    where Ω=(α,β,γ) is the Euler angle, R^(Ω) is the rotational operator, PS(x) is the S-th polynomial, K is the momentum operator of the whole system and T^R is the translational operators corresponding to the translational vector R, G^α is the point group operator, and pα is the parity operator, respectively. The details of Pdh(2) and Pdh(4) are shown in [Tahara2008 ]. The one body part of the wavefunction is represented as the pair function of the real space:

    |ϕpair=[i,j=1Nsσ1,σ2fiσ1jσ2ciσ1cjσ2]N/2|0,

    where N is the number of electrons and Ns is the number of sites. The setting for optimizing variational parameters or not is given by the following files (the parameters for LS are specified in the ModPara file).

    Gutzwiller (gutzwilleridx.def): Set the target parameters gi in PG to be optimized.

    Jastrow (jastrowidx.def): Set the target parameters vij in PJ to be optimized.

    DH2: Set the target 2-site doublon-holon correlation factor α2ntd(h) in Pdh(2) to be optimized.

    DH4: Set the target 4-site doublon-holon correlation factor α4ntd(h) in Pdh(4) to be optimized.

    GeneralRBM_PhysLayer: Set the target variational parameters aiσ in the RBM correlation factor NGeneralRBM.

    GeneralRBM_HiddenLayer: Set the target variational parameters hk in the RBM correlation factor NGeneralRBM.

    GeneralRBM_PhysHidden: Set the target variational parameters Wiσk in the RBM correlation factor NGeneralRBM.

    Orbital/OrbitalAntiParallel (orbitalidx.def): Set the pair orbital with anti-parallel spins fij in |ϕpair to be optimized.

    OrbitalParallel: Set the pair orbital with anti-parallel spins fiσjσ in |ϕpair to be optimized.

    OrbitalGeneral: Set the pair orbital with anti-parallel spins fiσjσ in |ϕpair to be optimized.

    TransSym (qptransidx.def): Set the the momentum projection operators LK and the lattice translational projection operators LP.

  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 gi in PG.

    InJastrow: Set the initial values of vij in PJ.

    InDH2: Set the initial values of α2ntd(h) in Pdh(2).

    InDH4: Set the initial values of α4ntd(h) in Pdh(4).

    InGeneralRBM_PhysLayer: Set the initial values of aiσ in the RBM correlation factor NGeneralRBM.

    InGeneralRBM_HiddenLayer: Set the initial values of hk in the RBM correlation factor NGeneralRBM.

    InGeneralRBM_PhysHidden: Set the initial values of Wiσk in the RBM correlation factor NGeneralRBM.

    InOrbital /InOrbitalAntiParallel: Set the initial values of fij in |ϕpair.

    InOrbitalParallel: Set the initial values of fiσjσ in |ϕpair.

    InOrbitalGeneral: Set the initial values of fiσjσ in |ϕpair.

  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.

GeneralRBM_PhysLayer

A part of the general RBM correlation factor including variational parameters in a physical layer αiσ.

GeneralRBM_HiddenLayer

A part of the general RBM correlation factor including variational parameters in a hidden layer hk.

GeneralRBM_PhysHidden

A part of the general RBM correlation factor including variational parameters which connect physical and hidden layers Wiσk.

Orbital

Pair orbital factors with anti-parallel spins fij.

OrbitalAntiParallel

Pair orbital factors with anti-parallel spins fij.

OrbitalParallel

Pair orbital factors with parallel spins fiσjσ.

OrbitalGeneral

Pair orbital factors fiσ1jσ2.

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.

InGeneralRBM_PhysLayer

Initial values of variational parameters of the general RBM correlation factors in a physical layer αiσ.

InGeneralRBM_HiddenLayer

Initial values of variational parameters of the general RBM correlation factors in a hidden layer hk.

InGeneralRBM_PhysHidden

Initial values of variational parameters of the general RBM correlation factors which connect physical and hidden layers Wiσk.

InOrbital

Initial values of pair orbital factors fij.

InOrbitalAntiParallel

Initial values of pair orbital factors fij.

InOrbitalParallel

Initial values of pair orbital factors fiσjσ.

InOrbitalGeneral

Initial values of pair orbital factors fiσ1jσ2.

OneBodyG

Output components for Green functions ciσcjσ

TwoBodyG

Output components for Correlation functions ciσcjσckτclτ

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 2Sz. Since the electrons form pair, 2Sz must be even number.

  • NSPGaussLeg

    Type : int-type (Positive integer, default value: 8)

    Description : The mesh number for the Gauss-legendre quadrature about β integration (Sy 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 εwf 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 ε 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 OkOl (0: off, 1: on). This speeds up calculation but increases the amount of memory usage from O(Np2) to O(Np2)+O(NpNMCS), where Np is the number of the variational parameters and NMCS 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(Np2)+O(NpNMCS) to O(Np)+O(NpNMCS) when Np>NMCS.

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 [ 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 [ int02 ].

Trans file (trans.def)

The Hamiltonian for general one-body interactions

HT=ijσ1σ2tijσ1σ2ciσ1cjσ2,

is added to the whole Hamiltonian by setting the parameters tijσ1σ2. 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 [ 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 tijσ1σ2.

  • [ double02 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for an imaginary part of tijσ1σ2.

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, tijσ1σ2=tjiσ2σ1.

InterAll file

The Hamiltonian for general two-body interactions

HI=i,j,k,lσ1,σ2,σ3,σ4Iijklσ1σ2σ3σ4ciσ1cjσ2ckσ3clσ4.

is added to the whole Hamiltonian by setting the parameters Iijklσ1σ2σ3σ4. 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 [ 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 Iijklσ1σ2σ3σ4.

  • [ double02 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for an imaginary part of Iijklσ1σ2σ3σ4.

Use rules

  • Headers cannot be omitted.

  • Since Hamiltonian must be Hermitian, the following relation must be satisfied, Iijklσ1σ2σ3σ4=Ilkjiσ4σ3σ2σ1.

  • 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

HU=iUinini

is added to the whole Hamiltonian by setting Ui. 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 [ int02 ] < Nsite).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for Ui.

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

HV=i,jVijninj

is added to the whole Hamiltonian by setting Vij. 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 [ int02 ], [ int03 ] < Nsite).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for Vij.

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

HH=i,jJijHund(ninj+ninj)

is added to the whole Hamiltonian by setting the parameters JijHund. 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 [ int02 ], [ int03 ] < Nsite).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for JijHund.

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

HP=i,jJijPair(cicjcicj+cjcicjci)

is added to the whole Hamiltonian by setting the parameters JijPair. 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 [ int02 ], [ int03 ] < Nsite).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for JijPair.

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

HE=i,jJijEx(cicjcjci+cicjcjci)

is added to the whole Hamiltonian by setting JijEx. 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 [ int02 ], [ int03 ] < Nsite).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : A value for JijEx.

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

PG=exp[iginini].

A site number i and the variational parameters gi 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 Ns and variational parameters as Ng, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns): [int03] [int04]

  • Lines (6+ Ns) - (5+ Ns + Ng): [int05] [int06]

Parameters

  • [ string01 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for total number of variational parameters gi. 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 gi.

  • [ string02 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for indicating the double or complex type of variational parameters gi. 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 gi (0: double, 1: complex).

  • [ int03 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a site index (0 [ int03 ] < Nsite).

  • [ int04 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters gi (0 [ int04 ] < [ int01]).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters (0 [ 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

PJ=exp[12ijvij(ni1)(nj1)]

Site numbers i j, and the variational parameters vij 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 Ns and variational parameters as Nj, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns×(Ns1)): [int03] [int04] [int05]

  • Lines (6+ Ns×(Ns1)) - (5+ Ns×(Ns1) + Nj): [int06] [int07]

Parameters

  • [ string01 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for total number of variational parameters vij. 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 vij.

  • [ string02 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for indicating the double or complex type of variational parameters vij. 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 vij (0: double, 1: complex).

  • [ int03 ], [ int04 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a site index (0 [ int03 ], [ int04 ] < Nsite).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters vij (0 [ int05 ] < [ int01]).

  • [ int06 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters (0 [ 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

Pdh(2)=exp[tn=02(α2ntdiξi2ntd+α2nthiξi2nth)].

A site number i, the two sites around i site and the variational parameters α2ntd(h) which have t kinds at each sites are specified. The details of the parameters α2ntd(h) and the operator ξi2ntd(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 Ns and variational parameters as Ndh2, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns×Ndh2): [int03] [int04] [int05] [int06]

  • Lines (6+ Ns×Ndh2) - (5+ (Ns+6)×Ndh2): [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 [ int03 ], [ int04 ], [ int05 ] < Nsite).

  • [ int06 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters (0 [ int06 ] < [ int01]).

  • [ int07 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters. The value is (2n+s)× [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, [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

Pdh(4)=exp[tn=04(α4ntdiξi4ntd+α4nthiξi4nth)]

A site number i, the four sites around i site and the variational parameters α4ntd(h) which have t kinds at each sites are specified. The details of the parameters α4ntd(h) and the operator ξi4ntd(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 Ns and variational parameters as Ndh4, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns×Ndh4): [int03] [int04] [int05] [int06] [int07] [int08]

  • Lines (6+ Ns×Ndh4) - (5+ (Ns+10)×Ndh4): [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 [ int03 ],,[ int07 ] < Nsite).

  • [ int08 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters (0 [ int08 ] < [ int01]).

  • [ int09 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters. The value is (2n+s)× [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, [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,

NGeneralRBM=exp[iaiσniσ]kNneuronGeneralcosh[bk+iσWiσkniσ]

this file sets the calculation conditions of exp[iaiσniσ].Asiteindex:math:i, a spin index σ and the variational parameters aiσ 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 Ns and variational parameters as Nv, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ 2Ns): [int03] [int04] [int05]

  • Lines (6+ 2Ns ) - (5+ 2Ns + Nv): [int06] [int07]

Parameters

  • [ string01 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for total number of variational parameters aiσ. 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 aiσ.

  • [ string02 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for indicating the double or complex type of variational parameters aiσ. 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 aiσ (0: double, 1: complex).

  • [ int03 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a site index (0 [ 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 vij (0 [ int05 ] < [ int01]).

  • [ int06 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters (0 [ 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=1 and Orbital. 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.

GeneralRBM_HiddenLayer file

In the general RBM correlation factors,

NGeneralRBM=exp[iaiσniσ]kNneuronGeneralcosh[bk+iσWiσkniσ]

this file sets the calculation conditions of bk in kNneuronGeneralcosh[bk+iσWiσkniσ].Ahiddenneuronindex:math:k and the variational parameters hk are specified. An example of the file format is shown as follows.

--------------------
NRBM_HiddenLayerIdx 2
ComplexType 1
k RBM_HiddenLayer_Idx
--------------------
 0  0
 1  0
 2  0
 3  0
 (continue...)
 0    1
 1    1

File format

In the following, we define the total number of neurons as NneuronGeneral and variational parameters as Nv, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+:math:N_{rm neuronGeneral}): [int03] [int04]

  • Lines (6+ NneuronGeneral ) - (5+ NneuronGeneral + Nv): [int05] [int06]

Parameters

  • [ string01 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for total number of variational parameters hk. 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 hk.

  • [ string02 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for indicating the double or complex type of variational parameters hk. 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 hk (0: double, 1: complex).

  • [ int03 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a neuron index (0 [ int03 ] < NneuronGeneral).

  • [ int04 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters hk (0 [ int05 ] < [ int01]).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters (0 [ int06 ] < [ int01]).

  • [ int06 ]

    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=1 and Orbital. 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 ] - [ int06 ] are out of range from the defined values.

GeneralRBM_PhysHidden file

In the general RBM correlation factors,

NGeneralRBM=exp[iaiσniσ]kNneuronGeneralcosh[bk+iσWiσkniσ]

this file sets the calculation conditions of Wiσk in kNneuronGeneralcosh[bk+iσWiσkniσ].Asiteindex:math:i, a spin index σ, a hidden neuron index k and the variational parameters Wiσk are specified. An example of the file format is shown as follows.

--------------------
NRBM_HiddenLayerIdx 32
ComplexType 1
i s k RBM_PhysHidden_Idx
--------------------
 0  0   0   0
 0  1   0   1
 1  0   0   2
 1  1   0   3
 2  0   0   4
 2  1   0   5
 (continue...)
 0    1
 1    1
 (continue...)

File format

In the following, we define the total number of sites as Ns, the total number of neurons as NneuronGeneral and variational parameters as Nv.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+:math:2 N_s N_{rm neuronGeneral}): [int03] [int04] [int05] [int06]

  • Lines (6+ 2NsNneuronGeneral ) - (5+ 2NsNneuronGeneral + Nv): [int07] [int08]

Parameters

  • [ string01 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for total number of variational parameters Wiσk. 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 Wiσk.

  • [ string02 ]

    Type : string-type (blank parameter not allowed)

    Description : A keyword for indicating the double or complex type of variational parameters Wiσk. 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 Wiσk (0: double, 1: complex).

  • [ int03 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a site index (0 [ int03 ] < Nsite).

  • [ int04 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a spin index ([ int03 ] = 0 or 1 ).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a neuron index (0 [ int03 ] < NneuronGeneral).

  • [ int06 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters Wiσk (0 [ int05 ] < [ int01]).

  • [ int07 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of variational parameters (0 [ 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

  • 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=1 and Orbital. 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 ] - [ int06 ] are out of range from the defined values.

Orbital/OrbitalAntiParallel file (orbitalidx.def)

This file sets the calculation conditions of pair orbitals

|ϕpair=[i,j=1Nsfijcicj]N/2|0.

Site numbers i,j and the variational parameters fij 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 Ns and variational parameters as No, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns2): [int03] [int04] [int05] [int06]

  • Lines (6+ Ns2 )- (5+ Ns2+No): [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 [ int03 ], [ int04 ] < Nsite).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters (0 [ 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 fij is specified by setting [ int06 ]=±1. 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 [ 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

|ϕpair=[i,j=1Nsσfiσjσciσcjσ]N/2|0.

Site numbers i,j, the spin index σ and the variational parameters fiσjσ are indicated. The indexes of fiσjσ 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 Ns and variational parameters as No, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Ns(Ns1)/2): [int03] [int04] [int05] [int06]

  • Lines (6+ Ns(Ns1)/2 )- (5+ Ns(Ns1)/2+No): [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 [ int03 ], [ int04 ] < Nsite).

  • [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters (0 [ 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 fij is specified by setting [ int06 ]=±1. 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 [ 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

|ϕpair=[i,j=1Nsσ1,σ2fiσ1jσ2ciσ1cjσ2]N/2|0.

Site numbers i,j, spin indexes σ1,σ2 and the variational parameters fiσ1jσ2 are indicated. The indexes of fiσ1jσ2 must satisfy the condition i+σ1Ns<j+σ2Ns, where σi=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 Ns and variational parameters as No, respectively. A total number of variational parameters Np is given by Ns2, 2Ns2Ns in Sz conserved and Sz unconserved system, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Line 3: [string02] [int02]

  • Lines 4 - 5: Header

  • Lines 6 - (5+ Np): [int03] [int04] [int05] [int06] [int07] [int08]

  • Lines (6+ Np) - (5+ Np+No): [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 [ int03 ], [ int04 ] < Nsite).

  • [ int04 ], [ int06 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a spin index (0:↑ spin, 1:↓ spin).

  • [ int07 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer setting kinds of variational parameters (0 [ 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 fiσ1jσ2 is specified by setting [ int08 ]=±1. 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 [ 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 LK=1NsReiKRT^R and lattice translational projection LP=αpαG^α. The patterns of projection are indicated by (α,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 Ns and projection patterns as NTS, respectively.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Lines 3 - 5: Header

  • Lines 6 - (5+ NTS): [int02] [double01] [double02]

  • Lines (6+ NTS) - (5+ (Ns+1)×NTS): [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 (α,R) (0 [ int02 ] < [ int01]).

  • [ double01 ]

    Type : double-type (blank parameter not allowed)

    Description : The weight Real part of pαcos(KR) of the projection pattern (α,R).

  • [ double02 ]

    Type : double-type (blank parameter not allowed)

    Description : The weight Imaginary part of pαcos(KR) of the projection pattern (α,R).

  • [ int03 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving kinds of the projection pattern (α,R) (0 [ int03 ] < [ int01]).

  • [ int04 ], [ int05 ]

    Type : int-type (blank parameter not allowed)

    Description : An integer giving a site index (0 [ 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 ] =±1. 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, 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.

======================
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 Nv.

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Lines 3 - 5: Header

  • Lines 6 - (5+ Nv): [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 [ 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 ciσ1cjσ2. 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 [ 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 ciσ1cjσ2ckσ3clσ4. 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 [ 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.