Non-Abelian topological order with SO(5)$_{1}$ chiral edge states

TL;DR

This paper constructs a chiral spin liquid with non-Abelian anyons, revealing emergent SO(5) symmetry in its edge states, confirmed through conformal field theory and tensor network methods, with detailed entanglement spectrum analysis.

Contribution

It introduces a new chiral spin liquid state with SO(5)$_{1}$ edge symmetry, supported by CFT analysis and tensor network simulations, highlighting novel edge state structures.

Findings

Edge states exhibit SO(5)$_{1}$ symmetry as shown by CFT counting.

Tensor network methods confirm the entanglement spectrum features.

Multiple branches in the entanglement spectrum are observed and analyzed.

Abstract

We consider a chiral spin liquid constructed using the parton theory. This state supports non-Abelian anyons and neutral fermions, which share some similarities with the celebrated Moore-Read state. The edge physics of the parton state and the Moore-Read state is very different. Based on conformal field theory (CFT) analysis, it is proposed that the edge states exhibit an emergent SO(5) symmetry. The counting of edge states in the low-lying SO(5)$_{1}$ CFT towers is computed. The chiral spin liquid is generated using tensor network methods, which allows us to confirm the SO(5)$_{1}$ counting using entanglement spectrum. An additional feature of multiple branches in the entanglement spectrum is observed and analyzed.