Simulation of anyons with tensor network algorithms

TL;DR

This paper adapts tensor network algorithms, specifically MERA, for simulating systems of anyons, enabling the study of their properties and potential for quantum computation.

Contribution

It introduces a method to modify tensor network algorithms for anyonic systems, demonstrated with Fibonacci anyons in 1D, aligning results with conformal field theory.

Findings

Successfully adapted MERA for Fibonacci anyons

Computed scaling dimensions consistent with conformal field theory

Paves the way for simulating large anyonic systems in 1D and 2D

Abstract

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.