Topological orders with classical Lie group symmetries from coupling electron wires

TL;DR

This paper constructs and analyzes topological orders with classical Lie group symmetries using coupled electron wire models, revealing new non-Abelian anyonic states and their properties.

Contribution

It provides a systematic, model-based derivation of non-Abelian topological states with Lie group symmetries, extending previous work on bosonic quantum Hall states.

Findings

Constructed states with SU(m)_n, SO(m)_n, and Sp(m)_n topological order.

Derived string operators for non-Abelian anyons.

Connected models to quantum Hall states, topological superconductors, and spin liquids.

Abstract

We study the topological order that arises from chiral states with ${\rm SU}(N)$ or ${\rm SO}(N)$ edge-state symmetry. This extends our previous study of topological orders that descend from the bosonic $E_8$ quantum Hall state. We use exactly solvable models of coupled electron wires to construct states with ${\rm SU}(m)_n$, ${\rm SO}(m)_n$, or ${\rm Sp}(m)_n$ topological order for various levels $n$. We use our constructions to write down string operators for various non-Abelian anyons. We thereby provide a systematic, model derivation of quantum Hall states, topological superconductors, and spin liquids with emergent non-Abelian quasiparticle excitations, including those of Ising, metaplectic, and Fibonacci type.