Exchange file

This file determines the values of Exchange couplings \(J_{ij}^{\rm Ex}\) (for \(S=1/2\) system).

Note

For spinless fermion models (CalcModel=7, 8), Exchange interactions have no physical meaning since there are no spin degrees of freedom. Specifying this file for spinless fermion models will result in an error.

For the fermion electronic system, the exchange terms are given as

(4.13)\[\mathcal H+=\sum_{i,j}J_{ij}^{\rm Ex} (c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow}+c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow}),\]

while for the spin system, they are given as

(4.14)\[\mathcal H+=\sum_{i,j}J_{ij}^{\rm Ex} (S_ {i}^{+}S_{j}^{-} + S_ {i}^{-}S_{j}^{+}).\]

We note that \((S_i^{+}S_j^{-} + S_i^{-}S_j^{+})\) in the spin system is written by the operators for electrons as \(-(c_ {i \uparrow}^{\dagger}c_{j\uparrow}c_{j \downarrow}^{\dagger}c_{i \downarrow} +c_ {i \downarrow}^{\dagger}c_{j\downarrow}c_{j \uparrow}^{\dagger}c_{i \uparrow})\). An example of the file format is as follows.

======================
NExchange 6
======================
========Exchange ======
======================
   0     1  0.50000
   1     2  0.50000
   2     3  0.50000
   3     4  0.50000
   4     5  0.50000
   5     0  0.50000

File format

• Line 1: Header

• Line 2: [string01] [int01]

• Lines 3-5: Header

• Lines 6-: [int02] [int03] [double01].

Parameters

• [string01]

  Type : String (a blank parameter is not allowed)

  Description : A keyword for the total number of Exchange couplings. 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 Exchange couplings.

• [int02], [int03]

  Type : Int (a blank parameter is not allowed)

  Description : An integer giving a site index (\(0<=\) [int02], [int03] \(<\) Nsite).

• [double01]

  Type : Double (a blank parameter is not allowed)

  Description : A value for \(J_{ij}^{\rm Ex}\).

Use rules

• Headers cannot be omitted.

• A program is terminated when the components of the exchange couplings are double counted.

• A program is terminated when [int01] is different from the total number of exchange couplings defined in this file.

• A program is terminated when either [int02] or [int03] is outside the range of the defined values.