2.2.1. Parameter file

The parameter file specifies calculation conditions of H-wave in TOML format. This file consists of these three sections:

1. mode section to set calculation mode,

2. log section to set standard log output,

3. file section to set file and directory paths. This section consists of two subsections, input and output.

A sample file reads as follows:

[log]
print_level = 1
print_step = 20
[mode]
mode = "UHFr"
[mode.param]
Nsite = 8
2Sz = 0
Ncond = 8
IterationMax = 1000
EPS = 8
RndSeed = 123456789
T = 0.0
[file]
[file.input]
path_to_input = ""
OneBodyG = "greenone.def"
[file.input.interaction]
Trans = "trans.def"
CoulombIntra = "coulombintra.def"
[file.output]
path_to_output = "output"
energy = "energy.dat"
eigen = "eigen"
green = "green.dat"

File format

TOML

Parameters

mode section

• mode

  Type : String

  Description : This parameter specifies calculation mode. Set to UHFr when using coordinate-space UHF.

• flag_fock

  Type : Boolean (default value is true)

  Description : When this parameter is true, the Fock term is considered. If it is false, only the Hartree term is considered.

mode.param section

mode.param section sets parameters of the calculation.

• T

  Type : Float (default value is 0)

  Description : This parameter specifies temperature. It must be greater than or equal to zero.

• 2Sz

  Type : Integer, String, or None (default value is None)

  Description : Twice the size of the \(z\) compoonent of the total spin is specified when it is set to a fixed value. In this case, the up and down spin components are calculated separately. If this parameter is not given, or it is set to "free", the spin space is not separated in the calculation.

  This parameter should not be specified when Sz is not conserved (e.g. when the spin-orbital interaction is present).

  2Sz takes a value between -Nsite and Nsite.

• Nsite

  Type : Integer

  Description : This parameter specifies the number of sites. It must be greater than or equal to one.

• Ncond

  Type : Integer

  Description : This parameter specifies the number of conduction electrons. It must be greater than or equal to one.

• filling

  Type : Float

  Description : This parameter specifies the filling ratio of electrons with respect to the number of states. It must be between 0 and 1. Both Ncond and filling are specified, the program will be terminated with error.

• Ncond_round_mode

  Type : String (default value is "strict")

  Description : This parameter specifies how the number of electrons calculated from the filling parameter is rounded to an integer value. The parameter must take one of the following values.

  • as-is: the value is not rounded to an integer. (returns a floating-point number)

  • round-up: the value is rounded up.

  • round-down: the value is rounded down.

  • round-off: the value is rounded to the closest integer. (0.5 is rounded up.)

  • round: the value is rounded by round function. (0.5 is rounded down.)

  • strict: if the value is not an integer value, the program terminates with error.

  • exact: if the value is not an integer value, a warning message will be shown and the value is rounded to an integer as round.

• IterationMax

  Type : Integer (default value is 20000)

  Description : This parameter specifies the maximum number of iterations. It must be greater than or equal to zero.

• EPS

  Type : Integer (default value is 6)

  Description : This parameter specifies the convergence criterion. The solver iteration will be terminated when the norm of the difference between the previous and new Green’s function falls below \(10^{\rm -EPS}\). The residue is defined by \(R = \sum_{i,j}^{N}\sqrt{ \left| G_{ij}^{\rm new} - G_{ij}^{\rm old} \right|^2} / 2N^2\). It must be greater than or equal to zero.

• Mix

  Type : Float (default value is 0.5)

  Description : This parameter specifies the ratio \(\alpha\) of simple-mixing when the Green’s function is updated by the previous and the new one. It must be between 0 and 1. If it is set to 1, the previous value will not be mixed. See Algorithms section for simple-mixing algorithm.

• RndSeed

  Type : Integer (default value is 1234)

  Description : This parameter specifies the seed of random numbers.

• ene_cutoff

  Type : Float (default value is 100.0)

  Description : This parameter specifies a cut-off to avoid overflow when the Fermi distribution function is calculated.

• strict_hermite

  Type : Boolean (default value is false)

  Description : This parameter specifies strictness of Hermiticity checks when the interaction definitions are read from files. If it is set to true, the program stops when the deviation larger than hermite_tolerance is detected. If it is set to false, a warning message will be shown and the program execution continues.

• hermite_tolerance

  Type : Float (default value is \(10^{-8}\))

  Description : This parameter specifies the tolerance of the deviation from Hermiticity condition \(|t_{ij} - t_{ji}^*| < \varepsilon\).

log section

• print_level

  Type : Integer (default value is 1)

  Description : This parameter specifies verbosity of the standard log output. When it is set to 1, the detailed information will be printed.

• print_step

  Type : Integer (default value is 1)

  Description : This parameter specifies the interval between outputs of calculation logs to the standard output during iterations. It must be greater than or equal to one.

• print_check

  Type : String

  Description : This parameter specifies the output logfile to which the calculation logs are written during the iterations besides the standard output. If it is not given, the logs are not exported to files.

file section

This section consists of input and output subsections. The former specifies settings on input files (e.g. locations and names of files), while the latter on output files, as described below.

file.input section

• path_to_input

  Type : String (default value is "")

  Description : This parameter specifies the directory in which the input files are located.

• Initial

  Type : String (default value is "")

  Description : This parameter specifies the input file for the initial configuration.

• OneBodyG

  Type : String (default value is "")

  Description : This parameter specifies the input file that contains a list of indices of one-body Green’s function to export.

file.input.interaction section

• Trans

  Type : String (default value is "")

  Description : This parameter specifies the input file for general one-body interaction term.

• InterAll

  Type : String (default value is "")

  Description : This parameter specifies the input file for generalized two-body interaction term.

• CoulombIntra

  Type : String (default value is "")

  Description : This parameter specifies the input file for on-site Coulomb interaction term.

• CoulombInter

  Type : String (default value is "")

  Description : This parameter specifies the input file for inter-site Coulomb interaction term.

• Hund

  Type : String (default value is "")

  Description : This parameter specifies the input file for Hund interaction term.

• PairHop

  Type : String (default value is "")

  Description : This parameter specifies the input file for pair-hopping term.

• Exchange

  Type : String (default value is "")

  Description : This parameter specifies the input file for exchange interaction term.

• Ising

  Type : String (default value is "")

  Description : This parameter specifies the input file for Ising interaction term.

• PairLift

  Type : String (default value is "")

  Description : This parameter specifies the input file for pair-lift interaction term.

file.output section

• path_to_output

  Type : String (default value is "output")

  Description : This parameter specifies the directory to store the output files.

• energy

  Type : String

  Description : This parameter specifies the output file for energies. If it is not given, the output is not exported.

• eigen

  Type : String

  Description : This parameter specifies the output file for eigenvalues of Hamiltonian. If it is not given, the output is not exported.

• green

  Type : String

  Description : This parameter specifies the output file for one-body Green’s function. If it is not given, the output is not exported.

• initial

  Type : String

  Description : This parameter specifies the output file for one-body Green’s function in a format suitable for the initial configuration. If it is not given, the output is not exported.

• fij

  Type : String

  Description : This parameter specifies the output file for pair-orbital factor \(f_{ij}\). If it is not given, the output is not exported.