NBodyInterAll file¶
This file determines generic N-body interaction terms added to the Hamiltonian. A line with \(N\) factors represents
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 \(i_p=j_p\). The factors are written in the order used by the operator product. An example of the file format is as follows.
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NNBodyInterAll 3
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========NBodyInterAll=====
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1 0 0 1 0 -1.0 0.0
1 1 0 0 0 -1.0 0.0
2 0 0 0 0 1 1 1 1 0.5 0.0
File format¶
Line 1: Header
Line 2: [string01] [int01]
Lines 3-5: Header
Lines 6-: [int02] ([int03] [int04] [int05] [int06]) … [double01] [double02]. 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 interaction terms. 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 interaction terms.
[int02]
Type : Int (a blank parameter is not allowed)
Description : The number of factors \(N\) in this term. 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).[double01]
Type : Double (a blank parameter is not allowed)
Description : A value for the real part of \(V\).
[double02]
Type : Double (a blank parameter is not allowed)
Description : A value for the imaginary part of \(V\).
Use rules¶
Headers cannot be omitted.
A program is terminated when [int01] is different from the total number of generic N-body interaction terms 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.
Diagonal NBodyInterAll terms must have a zero imaginary part.
Since the Hamiltonian must be Hermitian, off-diagonal NBodyInterAll terms must be written as adjacent Hermite-conjugate pairs. For fermion models, the conjugate line is written by reversing the factor order, swapping creation and annihilation indices in each factor, and using the complex-conjugate coefficient. For Spin/SpinGC, the strict Hermite-conjugate form, obtained by reversing the factor order, swapping the local-state indices, and using the complex-conjugate coefficient, is accepted. If all factors act on different sites, the spin operators commute, so the equivalent order-preserved form is also accepted.
For example, in a fermion model, the following two adjacent lines form a Hermite-conjugate pair:
2 0 0 1 0 2 1 3 1 0.25 0.10 2 3 1 2 1 1 0 0 0 0.25 -0.10
These lines correspond to
(4.10)¶\[\begin{split}\begin{aligned} &(0.25+0.10\mathrm{i}) c_{0,0}^{\dagger} c_{1,0} c_{2,1}^{\dagger} c_{3,1},\\ &(0.25-0.10\mathrm{i}) c_{3,1}^{\dagger} c_{2,1} c_{1,0}^{\dagger} c_{0,0}. \end{aligned}\end{split}\]In Spin/SpinGC, the strict Hermite-conjugate form can be written in the same way:
2 0 1 0 0 2 0 2 1 0.25 0.10 2 2 1 2 0 0 0 0 1 0.25 -0.10
With \(X_i^{ab}=|a\rangle_i\langle b|\), these lines correspond to the following operators. For spin-1/2, the same pair can also be written with \(S^\pm\).
(4.11)¶\[\begin{split}\begin{aligned} &(0.25+0.10\mathrm{i}) X_0^{1,0} X_2^{0,1} =(0.25+0.10\mathrm{i}) S_0^+ S_2^-,\\ &(0.25-0.10\mathrm{i}) X_2^{1,0} X_0^{0,1} =(0.25-0.10\mathrm{i}) S_2^+ S_0^-. \end{aligned}\end{split}\]Since the two factors act on different sites, the second line may also keep the same site order as the first line:
2 0 1 0 0 2 0 2 1 0.25 0.10 2 0 0 0 1 2 1 2 0 0.25 -0.10
This corresponds to the same Hermite-conjugate pair:
(4.12)¶\[\begin{aligned} &(0.25-0.10\mathrm{i}) X_0^{0,1} X_2^{1,0} =(0.25-0.10\mathrm{i}) S_0^- S_2^+ =(0.25-0.10\mathrm{i}) S_2^+ S_0^-. \end{aligned}\]NBodyInterAll is supported for SpinGC, Spin, HubbardGC, Hubbard, HubbardNConserved, SpinlessFermionGC, SpinlessFermion, tJGC, tJ, tJNConserved, KondoGC, Kondo, and KondoNConserved.
NBodyInterAll is not supported in TimeEvolution.
NBodyInterAll does not support CalcSpec for HubbardNConserved, tJNConserved, or KondoNConserved.
NBodyInterAll is not supported in FullDiag for SpinlessFermion/SpinlessFermionGC.
