Simulation of braiding anyons using Matrix Product States

TL;DR

This paper introduces a method combining U(1)-symmetry with anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on lattices, exploring braiding and entanglement properties.

Contribution

It extends MPS techniques to simulate anyonic systems with U(1)-symmetry at arbitrary densities, including braiding effects and entanglement analysis.

Findings

Ground state energies of Fibonacci anyons compared to bosons and fermions.

Entanglement entropy analysis reveals gapped and gapless phases.

Simulation of anyon dynamics on 1D chains and 2-leg ladders.

Abstract

Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.