4.2.17. PairExcitation file

The operators to generate the pair excited state \(c_{i\sigma_1}c_{j\sigma_2}^{\dagger}(c_{i\sigma_1}^{\dagger}c_{j\sigma_2})\) are defined. The type of pair excitation operators (\(c_{i\sigma_1}c_{j\sigma_2}^{\dagger}\) or \(c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\)) must be same in the input file. In the \(S_z\) conserved system, \(\sigma_1\) must be equal to \(\sigma_2\). An example of the file format is as follows.

===============================
NPair         24
===============================
======== Pair Excitation ======
===============================
    0     0     0     0    0    1.0    0.0
    0     1     0     1    0    1.0    0.0
    1     0     1     0    0    1.0    0.0
   (continue...)
   11     0    11     0    0    1.0    0.0
   11     1    11     1    0    1.0    0.0

File format

  • Line 1: Header
  • Line 2: [string01] [int01]
  • Lines 3-5: Header
  • Lines 6-: [int02]  [int03]  [int04]  [int05]  [int06]  [double01]  [double02].

Parameters

  • [string01]

    Type : String (a blank parameter is not allowed)

    Description : A keyword for the total number of the pair excitation operators. 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 pair excitation operators.

  • [int02], [int04]

    Type : Int (a blank parameter is not allowed)

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

  • [int03], [int05]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a spin index:
    For Hubbard or Kondo system, the index can be selected from
    0: Up-spin,
    1: Down-spin.
    For Spin system, the index can be selected from
    \(0, 1, \cdots, 2S+1\) (corresponding to -\(S-0.5, -S+0.5, \cdots S+0.5\)).

  • [int06]

    Type : Int (a blank parameter is not allowed)

    Description : An integer giving a type of pair excitation operators:
    0: \(c_{i\sigma_1}c_{j\sigma_2}^{\dagger}\)
    1: \(c_{i\sigma_1}^{\dagger}c_{j\sigma_2}\).

  • [double01], [double02]

    Type : Double (a blank parameter is not allowed)

    Description : [double01] gives the real part of \(c_{i\sigma_1}c_{j\sigma_2}^{\dagger} ( c_{i\sigma_1}^{\dagger}c_{j\sigma_2})\), while [double02] gives the imaginary part of \(c_{i\sigma_1}c_{j\sigma_2}^{\dagger} ( c_{i\sigma_1}^{\dagger}c_{j\sigma_2})\).

Use rules

  • Headers cannot be omitted.
  • A program is terminated when the components of the pair excitation operators are double counted.
  • A program is terminated when the conditions \(i=j\) and \(k=l\) are not satisfied for the spin model.
  • A program is terminated when [int01] is different from the total number of two-body Green’s functions defined in this file.
  • A program is terminated when [int02]-[int06] are outside the range of the defined values.