lattice-symmetries: A package for working with quantum many-body bases

TL;DR

lattice-symmetries is a software package that facilitates the use of symmetry-adapted bases in exact diagonalization of quantum many-body systems, significantly reducing computational complexity and enabling larger system analyses.

Contribution

it introduces a flexible package supporting arbitrary symmetries and operators, and demonstrates large-scale diagonalization for spin systems with minimal computational resources.

Findings

enables diagonalization of clusters with at least 42 sites on a single node

reduces effective Hilbert space dimension by symmetry considerations

makes large-scale exact diagonalization accessible to non-experts

Abstract

Exact diagonalization (ED) is one of the most reliable and established numerical methods of quantum many-body theory. The main limiting factor of the method is the exponential scaling of Hilbert space dimension with system size. Fortunately, by symmetry considerations the effective dimension can be reduced by multiple orders of magnitude. Here, we present lattice-symmetries, a package for working with such symmetry-adapted quantum many-body bases and operators. It supports bases for spin-1/2 particles with arbitrary user-defined symmetries and generic 1-, 2-, 3-, and 4-point operators. As an example application we discuss SpinED program which allows to easily diagonalize clusters of at least 42 sites on a single node thus making large-scale ED easily accessible to people with no background in numerical methods and computational physics.