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 LatticeModels

or

import Pkg; Pkg.add("LatticeModels")

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.

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.

Similar packages

Packages such as Quantica.jl, pybinding and Kwant provide similar functionality. And while they are all great packages, pybinding and Quantica are mostly focused on static properties of lattices. Kwant is more versatile, but its main focus is on quantum transport problems — it provides dynamic simulations in the Tkwant package, but LatticeModels.jl allows usage of various powerful backends, which improves performance and flexibility.

Here are some benchmarks:

Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 64 × Intel(R) Xeon(R) Platinum 8259CL CPU @ 2.50GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake-avx512)
Threads: 2 default, 0 interactive, 1 GC (on 64 virtual cores)

One can see dramatic performance improvements on small lattice sizes, while being competitive on larger ones. You can find the benchmarking code in the benchmarks folder of the package repository.

There are other nice features that LatticeModels.jl provides:

• 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.
• Full-fledged quantum mechanics. Any quantum operator can be defined and used in the simulations without much struggle.
• Manybody computations. LatticeModels.jl can handle manybody systems with particle interaction.