Classification of symmetry fractionalization in gapped $\mathbb Z_2$ spin liquids

TL;DR

This paper classifies the possible symmetry fractionalization patterns of spinons in gapped $ ext{Z}_2$ quantum spin liquids, providing a comprehensive framework for understanding different phases on kagome and triangular lattices.

Contribution

It derives a general constraint on symmetry fractionalization in gapped $ ext{Z}_2$ spin liquids with an odd number of spins per unit cell, enabling complete classification on specific lattices.

Findings

Derived a universal constraint on symmetry fractionalization

Classified all symmetric gapped $ ext{Z}_2$ spin liquids on kagome and triangular lattices

Provided a framework for distinguishing different spin liquid phases

Abstract

In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\mathbb{Z_2}$ spin liquids.