Tutorial

List of sample files

There are following tutorials in samples/Standard/.

  • The Hubbard model on the two dimensional square lattice

    (samples/Standard/Hubbard/square/)

  • The Hubbard model on the two dimensional triangular lattice

    (samples/Standard/Hubbard/triangular/)

  • The one dimensional Kondo chain

    (samples/Standard/Kondo/chain/)

  • The one dimensional antiferromagnetic Heisenberg chain

    (samples/Standard/Spin/HeisenbergChain/HeisenbergChain/)

  • The antiferromagnetic Heisenberg model on the two dimensional square lattice

    (samples/Standard/Spin/HeisenbergSquare/)

  • The antiferromagnetic Heisenberg model on the two dimensional Kagome lattice

    (samples/Standard/Spin/Kagome/)

We can perform these tutorials in the same way. In the following, the tutorial of the one dimensional antiferromagnetic Heisenberg chain is shown.

Heisenberg model

This tutorial should be performed in

sample/Standard/Spin/HeisenbergChain/.

This directory contains the following things:

The input file: StdFace.def

reference outputs: reference/

In this case, we treat the one dimensional antiferromagnetic Heisenberg chain which has a nearest neighbor spin coupling.

\[\begin{aligned} {\hat H} = J \sum_{i=1}^{L} {\hat {\boldsymbol S}}_i \cdot {\hat {\boldsymbol S}}_{i+1} \end{aligned}\]

The input file is as follows:

L = 16
Lsub=4
model = "Spin"
lattice = "chain lattice"
J = 1.0
2Sz = 0
NMPtrans=1

In this tutorial, J and the number of sites are set to 1 (arbitrary unit) and 16 respectively.

Running

We execute the following command.

$ mpiexec -np number-of-processes Path/vmcdry.out -s StdFace.def

The MPI command depends on your system (such as mpiexec, mpirun, mpijob, poe, etc.). Then, the calculation starts and the following standard message is outputted in the terminal.

######  Standard Intarface Mode STARTS  ######

  Open Standard-Mode Inputfile StdFace.def

  KEYWORD : l                    | VALUE : 16
  KEYWORD : lsub                 | VALUE : 4
  KEYWORD : model                | VALUE : spin
  KEYWORD : lattice              | VALUE : chain
  KEYWORD : j                    | VALUE : 1.0
  KEYWORD : nmptrans             | VALUE : 1

#######  Parameter Summary  #######

  @ Lattice Size & Shape

                L = 16
             Lsub = 4
                L = 16
                W = 1
           phase0 = 0.00000     ######  DEFAULT VALUE IS USED  ######

  @ Hamiltonian

               2S = 1           ######  DEFAULT VALUE IS USED  ######
                h = 0.00000     ######  DEFAULT VALUE IS USED  ######
            Gamma = 0.00000     ######  DEFAULT VALUE IS USED  ######
                D = 0.00000     ######  DEFAULT VALUE IS USED  ######
              J0x = 1.00000
              J0y = 1.00000
              J0z = 1.00000

  @ Numerical conditions

             Lsub = 4
             Wsub = 1
      ioutputmode = 1           ######  DEFAULT VALUE IS USED  ######

######  Print Expert input files  ######

    qptransidx.def is written.
         filehead = zvo         ######  DEFAULT VALUE IS USED  ######
         filehead = zqp         ######  DEFAULT VALUE IS USED  ######
      NVMCCalMode = 0           ######  DEFAULT VALUE IS USED  ######
     NLanczosMode = 0           ######  DEFAULT VALUE IS USED  ######
    NDataIdxStart = 1           ######  DEFAULT VALUE IS USED  ######
      NDataQtySmp = 1           ######  DEFAULT VALUE IS USED  ######
      NSPGaussLeg = 8           ######  DEFAULT VALUE IS USED  ######
         NMPTrans = 1
    NSROptItrStep = 1000        ######  DEFAULT VALUE IS USED  ######
     NSROptItrSmp = 100         ######  DEFAULT VALUE IS USED  ######
       NVMCWarmUp = 10          ######  DEFAULT VALUE IS USED  ######
     NVMCInterval = 1           ######  DEFAULT VALUE IS USED  ######
       NVMCSample = 1000        ######  DEFAULT VALUE IS USED  ######
    NExUpdatePath = 2
          RndSeed = 123456789   ######  DEFAULT VALUE IS USED  ######
       NSplitSize = 1           ######  DEFAULT VALUE IS USED  ######
           NStore = 0           ######  DEFAULT VALUE IS USED  ######
     DSROptRedCut = 0.00100     ######  DEFAULT VALUE IS USED  ######
     DSROptStaDel = 0.02000     ######  DEFAULT VALUE IS USED  ######
     DSROptStepDt = 0.02000     ######  DEFAULT VALUE IS USED  ######
          NSPStot = 0           ######  DEFAULT VALUE IS USED  ######
      ComplexType = 0           ######  DEFAULT VALUE IS USED  ######
    locspn.def is written.
    trans.def is written.
    interall.def is written.
    jastrowidx.def is written.
    coulombintra.def is written.
    coulombinter.def is written.
    hund.def is written.
    exchange.def is written.
    orbitalidx.def is written.
    gutzwilleridx.def is written.
    namelist.def is written.
    modpara.def is written.
    greenone.def is written.
    greentwo.def is written.

######  Input files are generated.  ######
-----------
Start: Read *def files.
  Read File namelist.def .
  Read File 'modpara.def' for ModPara.
  Read File 'locspn.def' for LocSpin.
  Read File 'trans.def' for Trans.
  Read File 'coulombintra.def' for CoulombIntra.
  Read File 'coulombinter.def' for CoulombInter.
  Read File 'hund.def' for Hund.
  Read File 'exchange.def' for Exchange.
  Read File 'gutzwilleridx.def' for Gutzwiller.
  Read File 'jastrowidx.def' for Jastrow.
  Read File 'orbitalidx.def' for Orbital.
  Read File 'qptransidx.def' for TransSym.
  Read File 'greenone.def' for OneBodyG.
  Read File 'greentwo.def' for TwoBodyG.
End  : Read *def files.
Start: Read parameters from *def files.
End  : Read parameters from *def files.
Start: Set memories.
End  : Set memories.
Start: Initialize parameters.
End  : Initialize parameters.
Start: Initialize variables for quantum projection.
End  : Initialize variables for quantum projection.
Start: Optimize VMC parameters.
End  : Optimize VMC parameters.
-----------

In the beginning of this run, files describing the detail of considered Hamiltonian

  • locspin.def

  • trans.def

  • coulombinter.def

  • coulombintra.def

  • exchange.def

  • hund.def

  • namelist.def

  • modpara.def

and files for setting variational parameters

  • gutzwilleridx.def

  • jastrowidx.def

  • orbitalidx.def

  • qptransidx.def

and files specifying elements of correlation functions that will be calculated

  • greenone.def

  • greentwo.def

are generated. The details of these files are shown in Input files for Expert mode.

During the calculation, the following files are outputted in output directory:

zvo_SRinfo.dat
zvo_out_001.dat
zvo_time_001.dat
zvo_var_001.dat
zvo_CalcTimer.dat

In zvo_out_001.dat, the following quantities are outputted at each bins

\[\langle H \rangle, \langle H^2 \rangle, \frac{\langle H^2 \rangle- \langle H \rangle^2 }{\langle H \rangle^2} \nonumber.\]

By seeing these informations, the conversion of the calculation can be judged. By using gnuplot, we can check the evolution of \(\langle H \rangle\) as follows:

gnuplot> plot "zvo_out_001.dat" u 1

The details of these outputted files are shown in Output files.

Output results

After finishing calculation normally, the files for the energy, the deviation, the optimized variational parameters and the time of execution for each calculation steps are outputted in output/ directory. In the following, the outputted files are shown

gutzwiller_opt.dat
jastrow_opt.dat
orbital_opt.dat
zqp_opt.dat
ClacTimer.dat

The details of these outputted files are shown in Output files.

Calculation of Green functions

After changing the value of NVMCCalMode from 0 to 1 in modpara.def file, we execute the following command. When we add "zqp_opt.dat" after "namelist.dat" as a command-line argument as follows, the calculation of Green functions is done by using the optimized variational parameters.

$ Path/vmc.out -e namelist.def output/zqp_opt.dat

After the calculation finishes, the following files are outputted in output/ directory.

zvo_cisajs_001.dat
zvo_cisajscktalt_001.dat

The details of these outputted files are shown in Output files.

Input files for Expert mode

In mVMC, the calculation is done by reading input files categorized by the following six parts.

  1. List: Specify the kinds and names of input files.

  2. Basic parameters: Specify the basic parameters.

  3. Set Hamiltonian: Specify the Hamiltonian.

  4. Set condition of variational parameters : Specify the variational parameters to be optimized.

  5. Initial variational parameters: Specify the initial values of the variational parameters.

  6. Output: Specify the components of one-body and two-body Green’s functions to be outputted.

The calculation for complex models can be done by directly making above input files. The details for each files are shown in Input files for Expert mode.

Fourier transformation of correlation functions

This package has a utility which performs the Fourier transformation of the correlation function and plots that function. For more details, please see HPhi/mVMC Fourier-Transformation utility.