LatticeModels.jl

This package provides a set of tools to simulate different quantum lattice systems.

Installation

Paste the following line into the Julia REPL:

]add https://github.com/aryavorskiy/LatticeModels.jl

or

import Pkg; Pkg.add(url="https://github.com/aryavorskiy/LatticeModels.jl")

Package features

• Bravais lattices with arbitrary geometry or boundary conditions.
• Powerful operator generation tools.
• Backend-independent computations: linear operators can be of any array type, allowing to use sparse or GPU arrays when needed.
• Manybody computations.
• Smart unitary evolution reducing excessive computations where possible.
• Supports visualization with Plots.jl.
• Compatible with QuantumOptics.jl.

Similar packages

Packages such as Quantica.jl, pybinding and Kwant provide similar functionality. However, they are in general designed for other purposes and lack some features that are present in LatticeModels.jl:

• Schrödinger equation solvers with time-dependent Hamiltonians. Only Kwant provides similar functionality with its Tkwant module, but it lacks the performance and flexibility in some cases.
• Convenient tools for setting periodic boundary conditions and gauge fields. The only way to do this in Kwant or Pybinding is to manually set the hopping values.
• A flexible interface for defining new types of lattices and bonds. Random lattices can be implemented on top of GenericLattice with ease.
• Manybody computations. LatticeModels.jl can handle manybody systems with particle interaction.

Overall, while Kwant and pybinding are mostly focused on quantum transport problems and Quantica.jl is designed to find various properties of lattices, LatticeModels.jl focuses on dynamic simulations.

Usage example

This simple code plots local density for lowest energy states of a square tight-binding lattice.

using LatticeModels, Plots

l = SquareLattice(40, 40)
H = tightbinding_hamiltonian(l)
diag = diagonalize(H)

n = 5
clims = (0, 0.0045)
p = plot(layout = @layout[ grid(n, n) a{0.1w}], size=(1000, 850))
for i in 1:n^2
    # Plot local density on each subplot
    E_rounded = round(diag.values[i], sigdigits=4)
    plot!(p[i], localdensity(diag[i]), title="\$E_{$i} = $E_rounded\$", st=:shape,
        clims=clims, c=:inferno, cbar=:none, lw=0, framestyle=:none, xlab="", ylab="")
end

# The following lines are kinda hacky; they draw one colorbar for all heatmaps
plot!(p[n^2+1], framestyle=:none)
scatter!([NaN], zcolor=[NaN], clims=clims, leg=:none, cbar=:right, subplot=n^2+2,
    framestyle=:none, inset=bbox(0.0, 0.05, 0.95, 0.9), background_subplot=:transparent)
savefig("example.png")

See more examples in the Examples section.