4.2.6. InterAll file

This file determines the values of generalized two-body interactions integrals \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\),

\[{\mathcal H}+=\sum_{i,j,k,l}\sum_{\sigma_1,\sigma_2, \sigma_3, \sigma_4} I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}.\]

For spin, the conditions \(i=j\) and \(k=l\) must be satisfied. An example of the file format is 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 (a blank parameter is not allowed)

    Description : A keyword for the total number of generalized two-body interactions. You can freely give a name to the keyword.

  • [int01]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving the total number of generalized two-body interactions.

  • [int02], [int04], [int06], [int08]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a site index (\(0<=\) [int02], [int04], [int06], [int08] \(<\) Nsite).

  • [int03], [int05], [int07], [int09]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a spin index:
    0: Up-spin,
    1: Down-spin.
  • [double01]

    Type : Double (a blank parameter is not allowed)

    Description : A value for a real part of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\).

  • [double02]

    Type : Double (a blank parameter is not allowed)

    Description : A value for an imaginary part of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\).

Use rules

  • Headers cannot be omitted.
  • Since the Hamiltonian must be Hermitian, the relation \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}=I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}^{\dagger}\) must be satisfied. A program is terminated when this relation is broken. It is noted that the term of the Hermitian conjugate for \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\) should be inputted as \(I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}\) \(c_{l\sigma_4}^{\dagger}c_{k\sigma_3}c_{j\sigma_2}^{\dagger}c_{i\sigma_1}\).
  • A program is terminated when the conditions \(i=j\) and \(k=l\) are not satisfied for the spin model.
  • A program is terminated when the components of the on-site interactions are double counted.
  • 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 outside the range of the defined values.