Tutorial¶

In this tutorial, we downfold Sr₂CuO₃ into single orbital 1D Hubbard model, and simulate that model with HPhi/mVMC. We use QuantumESPRESSO for the DFT calculation. Input files are served in samples/Wannier/Sr2CuO3 directory.

In actual studies, the input files etc. of each solver should be modified for more high accuracy calculation. Please refer to the manuals of each solver for the details of the input files.

SCF calculation of charge density¶

First, we perform the SCF calculation of the charge density. The input file is as follows:

scf.in

&CONTROL
 calculation = 'scf'
  pseudo_dir = '../pseudo'
prefix = 'sr2cuo3'
/
&SYSTEM
       ibrav = 0
         nat = 6
        ntyp = 3
     ecutwfc = 30.000000
     ecutrho = 240.000000
 occupations = 'tetrahedra_opt'
/
&ELECTRONS
mixing_beta = 0.3
/
CELL_PARAMETERS angstrom
 -1.749305 1.955690 6.351200
 1.749305 -1.955690 6.351200
 1.749305 1.955690 -6.351200
ATOMIC_SPECIES
 Sr 87.620000 Sr_ONCV_PBE-1.0.upf
 Cu 63.546000 Cu_ONCV_PBE-1.0.upf
 O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
 Sr 0.851940 0.351940 0.500000
 Sr 0.148060 0.648060 0.500000
 Cu 0.500000 0.000000 0.500000
 O 0.654110 0.154110 0.500000
 O 0.345890 0.845890 0.500000
 O 0.000000 0.000000 0.000000
K_POINTS automatic
 4 4 4 0 0 0

The pseudopotential (UPF file) are downloaded from The SG15 Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials. Put the pseudopotential files into ../pseudo directory.

http://www.quantum-simulation.org/potentials/sg15_oncv/sg15_oncv_upf_2015-10-07.tar.gz

We use the program pw.x in QuantumESPRESSO as follows.

$ pw.x -in scf.in

(Optional) Band structure¶

band.in

&CONTROL
 calculation = 'bands'
  pseudo_dir = '../pseudo'
prefix = 'sr2cuo3'
/
&SYSTEM
       ibrav = 0
         nat = 6
        ntyp = 3
     ecutwfc = 30.000000
     ecutrho = 240.000000
        nbnd = 35
/
&ELECTRONS
/
CELL_PARAMETERS angstrom
 -1.749305 1.955690 6.351200
 1.749305 -1.955690 6.351200
 1.749305 1.955690 -6.351200
ATOMIC_SPECIES
 Sr 87.620000 Sr_ONCV_PBE-1.0.upf
 Cu 63.546000 Cu_ONCV_PBE-1.0.upf
 O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
 Sr 0.851940 0.351940 0.500000
 Sr 0.148060 0.648060 0.500000
 Cu 0.500000 0.000000 0.500000
 O 0.654110 0.154110 0.500000
 O 0.345890 0.845890 0.500000
 O 0.000000 0.000000 0.000000
K_POINTS crystal
          50
        0.5000000000    0.5000000000   -0.5000000000    1.0
        0.4994075000    0.5005925000   -0.4428337500    1.0
        0.4988150000    0.5011850000   -0.3856675000    1.0
        0.4982225000    0.5017775000   -0.3285012500    1.0
        0.4976300000    0.5023700000   -0.2713350000    1.0
        0.4970375000    0.5029625000   -0.2141687500    1.0
        0.4964450000    0.5035550000   -0.1570025000    1.0
        0.4958525000    0.5041475000   -0.0998362500    1.0
        0.4952600000    0.5047400000   -0.0426700000    1.0
        0.5337666667    0.4662333333   -0.0811750000    1.0
        0.5722733333    0.4277266667   -0.1196800000    1.0
        0.6107800000    0.3892200000   -0.1581850000    1.0
        0.6492866667    0.3507133333   -0.1966900000    1.0
        0.6877933333    0.3122066667   -0.2351950000    1.0
        0.7263000000    0.2737000000   -0.2737000000    1.0
        0.6810400000    0.3189600000   -0.3189600000    1.0
        0.6357800000    0.3642200000   -0.3642200000    1.0
        0.5905200000    0.4094800000   -0.4094800000    1.0
        0.5452600000    0.4547400000   -0.4547400000    1.0
        0.5000000000    0.5000000000   -0.5000000000    1.0
        0.3333333333    0.3333333333   -0.3333333333    1.0
        0.1666666667    0.1666666667   -0.1666666667    1.0
        0.0000000000    0.0000000000    0.0000000000    1.0
        0.0000000000    0.0000000000    0.0625000000    1.0
        0.0000000000    0.0000000000    0.1250000000    1.0
        0.0000000000    0.0000000000    0.1875000000    1.0
        0.0000000000    0.0000000000    0.2500000000    1.0
        0.0000000000    0.0000000000    0.3125000000    1.0
        0.0000000000    0.0000000000    0.3750000000    1.0
        0.0000000000    0.0000000000    0.4375000000    1.0
        0.0000000000    0.0000000000    0.5000000000    1.0
        0.0426700000   -0.0426700000    0.5047400000    1.0
        0.0811750000   -0.0811750000    0.4662333333    1.0
        0.1196800000   -0.1196800000    0.4277266667    1.0
        0.1581850000   -0.1581850000    0.3892200000    1.0
        0.1966900000   -0.1966900000    0.3507133333    1.0
        0.2351950000   -0.2351950000    0.3122066667    1.0
        0.2737000000   -0.2737000000    0.2737000000    1.0
        0.2280833333   -0.2280833333    0.2280833333    1.0
        0.1824666667   -0.1824666667    0.1824666667    1.0
        0.1368500000   -0.1368500000    0.1368500000    1.0
        0.0912333333   -0.0912333333    0.0912333333    1.0
        0.0456166667   -0.0456166667    0.0456166667    1.0
        0.0000000000    0.0000000000    0.0000000000    1.0
        0.0833333333    0.0000000000    0.0000000000    1.0
        0.1666666667    0.0000000000    0.0000000000    1.0
        0.2500000000    0.0000000000    0.0000000000    1.0
        0.3333333333    0.0000000000    0.0000000000    1.0
        0.4166666667    0.0000000000    0.0000000000    1.0
        0.5000000000    0.0000000000   -0.0000000000    1.0

We use pw.x.

$ pw.x -in band.in

bands.in

&BANDS
      prefix = 'sr2cuo3'
       lsym = .false.
/

We use bands.x QuantumESPRESSO.

$ bands.x -in bands.in

We can plot the band structure by reading output bands.out.gnu from GnuPlot etc.

Kohn-Sham orbitals for Wannier¶

nscf.in

&CONTROL
 calculation = 'nscf'
  pseudo_dir = '../pseudo'
  wf_collect = .true.
      prefix = 'sr2cuo3'
/
&SYSTEM
       ibrav = 0
         nat = 6
        ntyp = 3
     ecutwfc = 30.000000
     ecutrho = 240.000000
 occupations = 'tetrahedra_opt'
        nbnd = 35
/
&ELECTRONS
/
CELL_PARAMETERS angstrom
 -1.749305 1.955690 6.351200
 1.749305 -1.955690 6.351200
 1.749305 1.955690 -6.351200
ATOMIC_SPECIES
 Sr 87.620000 Sr_ONCV_PBE-1.0.upf
 Cu 63.546000 Cu_ONCV_PBE-1.0.upf
 O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
 Sr 0.851940 0.351940 0.500000
 Sr 0.148060 0.648060 0.500000
 Cu 0.500000 0.000000 0.500000
 O 0.654110 0.154110 0.500000
 O 0.345890 0.845890 0.500000
 O 0.000000 0.000000 0.000000
K_POINTS automatic
 4 4 4 0 0 0

We use pw.x as

$ pw.x -in nscf.in

Then, we use the utility qe2respack.py which is included in the RESPACK package. The command-line argument is the name of [prefix].save directory.

$ qe2respack.py sr2cuo3.save

Wannier function, dielectric function, effective interaction¶

respack.in

&PARAM_CHIQW
Num_freq_grid = 1
!Ecut_for_eps = 
flg_cRPA = 1
/
&PARAM_WANNIER
N_wannier = 1
Lower_energy_window = 8
Upper_energy_window = 13
N_initial_guess = 1
/
dx2 0.2 0.500000 0.000000 0.50000 0.0 0.0 1.0  0.0 1.0 0.0 1.0 0.0 0.0
&PARAM_INTERPOLATION
N_sym_points = 10
!dense = 20, 24, 28
/
0.50000 0.50000 -0.50000
0.49526 0.50474 -0.04267
0.72630 0.27370 -0.27370
0.50000 0.50000 -0.50000
0.00000 0.00000 0.00000
0.00000 0.00000 0.50000
0.04267 -0.04267 0.50474
0.27370 -0.27370 0.27370
0.00000 0.00000 0.00000
0.50000 0.00000 0.00000
&PARAM_VISUALIZATION
flg_vis_wannier = 1,
ix_vis_min = -1,
ix_vis_max = 2,
iy_vis_min = -1,
iy_vis_max = 1,
iz_vis_min = -1,
iz_vis_max = 2
/
&PARAM_CALC_INT
calc_ifreq = 1
ix_intJ_min = -1
ix_intJ_max = 1
iy_intJ_min = -1
iy_intJ_max = 1
iz_intJ_min = -1
iz_intJ_max = 1
/

We use calc_wannier, calc_chiqw, calc_j3d, calc_w3d in RESPACK.

$ calc_wannier < respack.in
$ calc_chiqw < respack.in
$ calc_w3d < respack.in
$ calc_j3d < respack.in

After finishing calculations, the files are outputted in dir-model folder. The format of these files is Wannier90 format and the data such as the hopping integrals are written. (If you use the old version of RESPACK (20190226), the folder name is dir-mvmc .)

Quantum lattice mode for HPhi/mVMC¶

Using standard mode of HPhi/mVMC, the calculation will be done by reading the files in dir-model folder. First, the files in dir-model directory should be moved to the current directry. Then, the calculation will be started by using standard mode. For example, in HPhi, the calculation will be dobe by typing the following command:

stan.in

model = "Hubbard"
lattice = "wannier90"
a0w = 8
a0l = 0
a0h = 8
a1w = 0
a1l = 1
a1h = 0
a2w = 1
a2l = 0
a2h = 0
method = "TPQ"
nelec = 8
exct = 1
cutoff_t = 0.5
cutoff_u = 1.0
cutoff_j = 0.02

$ cp ./dir-model/* .
$ HPhi -s stan.in

Tutorial¶

SCF calculation of charge density¶

(Optional) Band structure¶

Kohn-Sham orbitals for Wannier¶

Wannier function, dielectric function, effective interaction¶

Quantum lattice mode for HPhi/mVMC¶

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