Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid

TL;DR

This paper investigates a non-Abelian spin-1 chiral spin liquid state using variational Monte Carlo, demonstrating its topological order and entanglement properties consistent with the Moore-Read state, and analyzing spin correlations and entanglement entropy.

Contribution

It provides a detailed numerical analysis of the topological and entanglement properties of a lattice non-Abelian spin liquid state based on the Moore-Read wave function.

Findings

Spin correlations become indistinguishable for large system sizes.

Topological entanglement entropy matches that of the Moore-Read state.

The lattice spin liquid exhibits the same topological order as the continuum Moore-Read state.

Abstract

We analyze the properties of a non-Abelian spin-1 chiral spin liquid state proposed by Greiter and Thomale [PRL 102, 207203 (2009)] using variational Monte Carlo. In this state the bosonic $\nu = 1$ Moore-Read Pfaffian wave function is used to describe a gas of bosonic spin flips on a square lattice with one flux quantum per plaquette. For toroidal geometries there is a three-dimensional space of these states corresponding to the topological degeneracy of the bosonic Moore-Read state on the torus. We show that spin correlations for different states in this space become indistinguishable for large system size. We also calculate the Renyi entanglement entropy for different system partitions to extract the topological entanglement entropy and provide evidence that the topological order of the lattice spin-liquid state is the same as that of the continuum Moore-Read state from which it is constructed.