InterAll file

This file determines the coefficients of the generalized two-body interaction integrals \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\) of the Hamiltonian

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

An example of the file format is presented below.

======================
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: [ninterall] [count]

  • Lines 3-5: Header

  • Lines 6-: [i] [s1] [j] [s2] [k] [s3] [l] [s4] [v.real] [v.imag]

Parameters

  • [ninterall]

    Type : String (blank is not allowed)

    Description : An arbitrary keyword for the total number of the two-body interactions.

  • [count]

    Type : Integer (blank is not allowed)

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

  • [i], [j], [k], [l]

    Type : Integer (blank is not allowed)

    Description : An integer giving a site index (\(0 \le i, j, k, l < {\rm Nsite}\)).

  • [s1], [s2], [s3], [s4]

    Type : Integer (blank is not allowed)

    Description : An integer giving a spin index: either 0 (up-spin) or 1 (down-spin).

  • [v.real], [v.imag]

    Type : Float (blank is not allowed)

    Description : Values for the real and imaginary parts of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}\), respectively.

Usage ruels

  • Headers cannot be omitted.

  • Since the Hamiltonian should be hermite, the coefficients must satisfy the relation \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}=I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1}^{\dagger}\). Otherwise, the program is terminated or a warning is reported, depending on the strict_hermite parameter. It is noted that the term of the Hermite 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 read \(I_{lkji\sigma_4\sigma_3\sigma_2\sigma_1} c_{l\sigma_4}^{\dagger}c_{k\sigma_3}c_{j\sigma_2}^{\dagger}c_{i\sigma_1}\).

  • The program is terminated with error if there are duplicated entries.

  • The program is terminated with error when the number of entries is different from [count].

  • The program is terminated with error if [i], [j], [k], [l], [s1], [s2], [s3], or [s4] are outside the range of the defined values.