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MPSKitModels.jl

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import Pkg
Pkg.add("MPSKitModels")

MPSKitModels.jl provides operators, tools and utilities for MPSKit.jl. The main goal is to facilitate the definition and readability of Hamiltonians on (1+0)-dimensional quantum systems, as well as their quasi-one-dimensional extensions, such as cylinders, ladders, etc. Additionally, some models from (2+0)-dimensional statistical mechanics are provided.

Overview

The main building blocks of these Hamiltonians are local N-body operators, which are provided in the form of an AbstractTensorMap{N,N} (see TensorKit.jl). Several often-used operators are defined and exported within MPSKitModels.jl:

  • spin operators (S_x, S_y, S_z, S_plus, S_min)
  • spin exchange operators (S_xx, S_yy, S_zz, S_exchange, S_plusmin, S_minplus)
  • bosonic operators (a_plus, a_min, a_number)
  • fermionic operators (c_plus, c_min, c_number)
  • fermionic spin operators (e_plus, e_min, e_number, e_number_up, e_number_down, e_number_updown)

These operators can then be combined to define Hamiltonians by way of the @mpoham macro. This transforms {} expressions to denote the site-indices upon which the operators act, and generates site-indices for various geometries. Some examples to showcase this:

using MPSKitModels, TensorKit

g = 1.0
H_ising = @mpoham sum(S_xx(){i, i + 1} + g * S_z(){i} for i in -Inf:Inf)

J = [1.0 -1.0]  # staggered couplings over unit cell of length 2
H_heisenberg_ = @mpoham sum(J[i] * S_exchange(SU2Irrep; spin=1){i, i + 1} for i in vertices(InfiniteChain(2)))

H_heisenberg_cylinder =
    @mpoham sum(J1 * S_exchange(; spin=1){i, j} for (i, j) in nearest_neighbours(InfiniteCylinder(3)))

J1 = 0.8
J2 = 0.2

H_J1J2 = @mpoham sum(J1 * S_exchange(){i, j} for (i, j) in nearest_neighbours(InfiniteCylinder(4))) +
    sum(J2 * S_exchange(){i,j} for (i, j) in next_nearest_neighbours(InfiniteCylinder(4)))

For convenience, several models have already been defined. The full list can be found in the docs.