Lattice spin models for non-Abelian Chiral Spin Liquids

TL;DR

This paper introduces two-dimensional lattice spin models that realize non-Abelian chiral spin liquids with gapped bulk and gapless edge states, extending the understanding of topological quantum phases.

Contribution

It proposes a new class of lattice Hamiltonians for non-Abelian SU(2) chiral spin liquids with analytically tractable properties.

Findings

Models exhibit a bulk energy gap.

Edge states are described by SU(2)$_n$ WZNW conformal field theory.

Construction from coupled spin ladders with multi-spin interactions.

Abstract

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge excitations described by the SU(2)$_n$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of a generalized spin-$n/2$ ladders with multi-spin exchange interaction which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)$_n$ gapless edge excitations.