3.2.1. Parameter files

The parameter file specifies calculation conditions and parameters for H-wave in TOML format. It is composed of the following three sections.

1. mode section for specifying calculation conditions,

2. log section for setting standard outputs,

3. file section for setting file paths: It contains input and output subsections.

An example of the file is shown below:

[log]
  print_level = 1
  print_step = 10
[mode]
  mode = "UHFk"
[mode.param]
  # 2Sz = 0
  Ncond = 16
  IterationMax = 1000
  EPS = 8
  Mix = 0.5
  RndSeed = 123456789
  # ene_cutoff = 1.0e+2
  T = 0.0
  CellShape = [ 4, 4, 1 ]
  SubShape = [ 2, 2, 1 ]
[file]
[file.input]
  path_to_input = ""
  # initial = "green_init.dat.npz"
[file.input.interaction]
  path_to_input = "./"
  Geometry = "geom.dat"
  Transfer = "transfer.dat"
  CoulombInter = "coulombinter.dat"
[file.output]
  path_to_output = "output"
  energy = "energy.dat"
  eigen = "eigen"
  green = "green"

File format

TOML format

Parameters

mode section

• mode

  Type : String

  Description : This parameter specifies the calculation mode. Set to "UHFk" for calculations of the wave-number space UHF.

• flag_fock

  Type : Boolean (Default value is true)

  Description : If true, include the Fock term in the Hamiltonian, otherwise, exclude it (Hartree approximation).

• enable_spin_orbital (default value is false)

  Type : Boolean

  Description : This parameter specifies whether to allow spin-orbital interaction. If it is set to true, the orbital indices in Transfer term are interpreted in the way that they include the orbital index \(\alpha\) and the spin index \(s\) by \(\alpha + N_\text{orb} \cdot s\).

mode.param section

mode.param section contains the parameters for the calculation.

• CellShape

  Type : Integer array

  Description : This parameter specifies the shape of the lattice Lx, Ly, Lz.

• SubShape

  Type : Integer array (default value is [ Lx, Ly, Lz ])

  Description : This parameter specifies the shape of the sublattice Bx, By, Bz.

• T

  Type : Float (default value is 0)

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

• 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. It is considered convergent when the norm of the difference between the previous and the 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 the simple-mixing algorithm.

• RndSeed

  Type : Integer (default value is 1234)

  Description : This parameter specifies the seed of the random number generator.

• ene_cutoff

  Type : Float (default value is 100.0)

  Description : This parameter specifies the cutoff to avoid overflow in the calculations of the Fermi distribution function.

• strict_hermite

  Type : Boolean (default value is false)

  Description : This parameter specifies the strictness of checking Hermiticity of the interaction definitions when they are read from files. If it is true, the program will be terminated with error when there are deviations greater than hermite_tolerance. If it is false, only the warning messages will be shown, and the calculation continues.

• hermite_tolerance

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

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

• trustme_interaction_range

  Type : Boolean (default value is false)

  Description :

  Relax the checks that the distances of hopping and interaction are within the halves of CellShape; if true, warn and continue execution, otherwise stop.

log section

• print_level

  Type : Integer (default value is 1)

  Description : This parameter specifies the verbosity of the standard output. If it is set to 1, a detailed information will be shown.

• print_step

  Type : Integer (default value is 1)

  Description : This parameter specifies the interval to write calculation logs to the standard output during the iteration. It must be greater than or equal to one.

• print_check

  Type : String (default value is None)

  Description : This parameter specifies the filename to which the calculation logs are written during the iteration besides the standard output. If it is not set, no output file will be generated.

file section

This section consists of input and output subsections. The former specifies the settings on the input files (such as locations and name of the files), and the latter on the output files (such as locations to store).

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

  Description : This parameter specifies the filename of the initial configuration of the one-body Green’s function. The input file is in NumPy binary format that corresponds to the output format of green in file.output section.

file.input.interaction section

This section describes the relation of the interaction types and geometry information to the definition files.

• path_to_input

  Type : String

  Description : This parameter specifies the directory in which the input files are located. It is independent from path_to_input in file.input section.

• Geometry

  Type : String

  Description : This parameter specifies the filename for the geometry information.

• Transfer, CoulombIntra, CoulombInter, Hund, Ising, Exchange, PairLift, PairHop

  Type : String

  Description : These parameters specify the filenames for the definitions of the corresponding interaction terms.

file.output section

• path_to_output

  Type : String (default value is "output")

  Description : This parameter specifies the directory in which the output files are stored.

• energy

  Type : String

  Description :

  This parameter specifies the name of the file to store the energy values. If it is not set, no output will be generated.

• eigen

  Type : String

  Description : This parameter specifies the name of the file to store the eigenvalues and eigenvectors of the Hamiltonian. If it is not set, no output will be generated.

• green

  Type : String (default value is "green")

  Description : This parameter specifies the name of the file to store the one-body Green’s functions. If it is set to an empty string, no output will be generated.

• rpa

  Type : String

  Description : This parameter specifies the name of the file to store the one-body term involving the approximated two-body interaction term by UHF method. The output may be used as an initial configuration of the RPA calculation by specifying it in the parameter file.input.trans_mod. If it is not set, no output will be generated.