NBodyG file

This file determines the target components of generic N-body Green’s functions. A line with \(N\) factors represents

(4.22)\[\left\langle \prod_{p=1}^{N} c_{i_p\sigma'_p}^{\dagger} c_{j_p\sigma_p} \right\rangle .\]

For Spin/SpinGC models, each factor represents a local spin matrix element on one site instead of a fermion bilinear, and the input must satisfy \(i_p=j_p\). An example of the file format is as follows.

==========================
NNBodyG 3
==========================
============NBodyG========
==========================
1 0 0 1 0
2 0 0 0 0 1 1 1 1
3 0 0 0 0 1 1 1 1 2 0 2 0

File format

  • Line 1: Header

  • Line 2: [string01] [int01]

  • Lines 3-5: Header

  • Lines 6-: [int02] ([int03] [int04] [int05] [int06]) … The group in parentheses is repeated [int02] times.

Parameters

  • [string01]

    Type : String (a blank parameter is not allowed)

    Description : A keyword for the total number of generic N-body Green’s functions. 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 generic N-body Green’s functions.

  • [int02]

    Type : Int (a blank parameter is not allowed)

    Description : The number of factors \(N\) in this component. It must be a positive integer.

  • [int03], [int05] of each factor

    Type : Int (a blank parameter is not allowed)

    Description : Site indices (\(0<=\) site index \(<\) Nsite). [int03] and [int05] correspond to \(i_p\) and \(j_p\), respectively.

  • [int04], [int06] of each factor

    Type : Int (a blank parameter is not allowed)

    Description : Spin or local-state indices.
    For Hubbard, tJ, Kondo, and their GC/NConserved variants:
    0: Up-spin,
    1: Down-spin.
    For Spin/SpinGC, use the same local-state index convention as OneBodyG and TwoBodyG.
    For SpinlessFermion/SpinlessFermionGC, only 0 is allowed (any non-zero index causes an error).

Use rules

  • Headers cannot be omitted.

  • A program is terminated when [int01] is different from the total number of generic N-body Green’s functions defined in this file.

  • A program is terminated when a site index or spin index is outside the allowed range.

  • For Spin/SpinGC, every factor must satisfy \(i_p=j_p\).

  • For Kondo/KondoGC/KondoNConserved, a factor involving a local-spin site must satisfy \(i_p=j_p\). General-spin Kondo local spins are not supported.

  • NBodyG is supported for SpinGC, Spin, HubbardGC, Hubbard, HubbardNConserved, SpinlessFermionGC, SpinlessFermion, tJGC, tJ, tJNConserved, KondoGC, Kondo, and KondoNConserved.

  • NBodyG is an equal-time expectation-value output and is not used as an excitation-operator input for CalcSpec. Use SingleExcitation or PairExcitation for dynamical correlation functions in CalcSpec.

  • In HubbardNConserved, tJNConserved, and KondoNConserved, using NBodyG together with CalcSpec is rejected.

  • The output values are written to the files described in NBodyG.dat.