MPSKitModels.jl

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-dimensional systems, as well as quasi-1-dimensional systems defined on a cylinder or infinite strips.

Overview

The main building blocks of these Hamiltonians are local N-body operators, which should be 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 (sigma_x, sigma_y, sigma_z, sigma_plus, sigma_min)
• spin exchange couplings (sigma_xx, sigma_yy, sigma_zz, sigma_exchange, sigma_plusmin, sigma_minplus)
• fermionic creation and annihilation operators (cc, ccdag, cdagc, cdagcdag, number)
• ...

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
h = 0.5
H_ising = @mpoham sum(sigma_xx(){i, i + 1} + h * sigma_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] * sigma_exchange(){i, i + 1} for i in -Inf:2:Inf)

H_heisenberg_cylinder =
    @mpoham sum(J1 * sigma_exchange(){i, j} for (i, j) in nearest_neighbours(InfiniteCylinder(3)))

J1 = 0.8
J2 = 0.2

H_J1J2 = @mpoham sum(J1 * sigma_exchange(){i, j} for (i, j) in nearest_neighbours(InfiniteCylinder(4))) +
    sum(J2 * sigma_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, along with all information in the docs.