Numerical simulation of non-abelian 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.
Keywords
Cite
@article{arxiv.2206.14730,
title = {Numerical simulation of non-abelian anyons},
author = {Nico Kirchner and Darragh Millar and Babatunde M. Ayeni and Adam Smith and Joost K. Slingerland and Frank Pollmann},
journal= {arXiv preprint arXiv:2206.14730},
year = {2023}
}
Comments
39 pages, 19 figures