4.2.20. TwoBodyTE File

This file determines the values of the two-body interactions \(I_{i\sigma_1j \sigma_2 k \sigma_3 l \sigma_4}(t)c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}\) at each time \(t\),

(4.19)\[{\mathcal H}(t) +=\sum_{ijkl}\sum_{\sigma_1\sigma_2\sigma_3\sigma_4} I_{i\sigma_1j \sigma_2 k \sigma_3 l \sigma_4}(t) c_{i\sigma_1}^{\dagger}c_{j\sigma_2}c_{k\sigma_3}^{\dagger}c_{l\sigma_4}.\]

An example of the file format is as follows.

==================================
AllTimeStep         100
==================================
===== TwoBody Time Evolution =====
==================================
    0.0   3
    0  1  0  1  0  0  0  0       1.0    0.0
    1  0  1  0  0  0  0  0       1.0    0.0
    1  0  1  0  2  0  2  0       1.0    0.0
    0.2   3
   (continue...)

File format

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Lines 3-5: Header

From line 6, time \(t\) and total number of transfer integrals \(N(t)\) are first defined and next the two-body interactions \(I_{i\sigma_1j \sigma_2 k \sigma_3 l \sigma_4}(t)\) are defined.

  • Line m: [double01]  [int02]

  • Lines (m+1) - (m+1+[int02]): [int03]  [int04]  [int05]  [int06]  [int07]  [int08]  [int09]  [int10]  [double02]  [double03]

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 time steps defined in this file.

  • [double01]

    Type : Double (a blank parameter is not allowed)

    Description : Time \(t\).

  • [int02]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving the total number of two-body interactions at time \(t\).

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

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a site index (\(0<=\) [int03],[int05],[int07],[int09] \(<\) Nsite).

  • [int04], [int06], [int08], [int10]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a spin index:
    0: Up-spin
    1: Down-spin.

  • [double02], [double03]

    Type : Double (a blank parameter is not allowed)

    Description : A value for real and imaginary part of \(I_{ijkl\sigma_1\sigma_2\sigma_3\sigma_4}(t)\) at time \(t\) is defined [double02] and [double03], respectively.

Use rules

  • Headers cannot be omitted.

  • A program is terminated when LanczosStep defined in ModPara is greater than [int02].

  • A program is terminated when [int03]-[int10] are outside the range of the defined values.