Anyonic entanglement renormalization

TL;DR

This paper introduces a variational ansatz for chains of anyons that leverages their unique Hilbert space structure, enabling efficient description of critical systems with non-abelian statistics, extending entanglement renormalization techniques.

Contribution

It develops a novel anyonic entanglement renormalization ansatz, generalizing the MERA framework to non-abelian anyons, and demonstrates its effectiveness on the golden chain model.

Findings

The ansatz accurately captures critical behavior in anyonic chains.

Numerical results validate the ansatz's ability to describe non-abelian exchange statistics.

Extension of entanglement renormalization to non-abelian anyons demonstrated.

Abstract

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions.