Numerical simulation of non-abelian anyons

TL;DR

This paper introduces a novel algorithm for simulating non-abelian anyons on 2D lattices, enabling analysis of their energy spectra and non-equilibrium dynamics, which was previously computationally challenging.

Contribution

The authors develop a topologically derived algorithm for simulating both abelian and non-abelian anyonic systems in two dimensions.

Findings

Level repulsion observed in energy spectra of Fibonacci and Ising anyons

Homogenization of density distribution indicating thermalization after quenches

Algorithm successfully models non-equilibrium dynamics of anyons

Abstract

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general abelian and non-abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons and Ising anyons. Additionally, we simulate non-equilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times - indicating thermalization.