Kagome chiral spin liquid as a gauged U(1) symmetry protected topological phase

TL;DR

This paper constructs a theoretical framework connecting kagome chiral spin liquids to gauged U(1) symmetry-protected topological phases, providing a lattice gauge theory derivation of the low-energy topological field theory.

Contribution

It offers an explicit lattice gauge theory construction of a kagome chiral spin liquid starting from a microscopic model and identifies the role of U(1) SPT phases in its formation.

Findings

Derived the continuum limit of the lattice gauge theory model.

Identified the U(1) SPT phase of bosonic spinons as crucial.

Proposed a general approach for understanding topological spin liquids.

Abstract

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well-established numerically, a controlled theoretical path from the lattice model leading to a low energy topological field theory is still lacking. This we provide via an explicit construction, starting from reformulating a microscopic model for a CSL as a lattice gauge theory, and deriving the low-energy form of its continuum limit. A crucial ingredient is the realisation that the bosonic spinons of the gauge theory exhibit a $U(1)$ symmetry-protected topological (SPT) phase, which upon promoting its $U(1)$ global symmetry to a local gauge structure ("gauging") yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of an SPT phase can be applied more generally to understand topological spin liquids.