Detecting crystal symmetry fractionalization from the ground state: Application to $\mathbb Z_2$ spin liquids on the kagome lattice

TL;DR

This paper introduces a method to detect crystal symmetry fractionalization in quantum spin liquids from ground state wave functions, aiding the classification of topologically ordered states, especially on the kagome lattice.

Contribution

The authors propose a simple, effective approach to identify symmetry fractionalization signatures directly from ground state wave functions, enabling classification of $ ext{Z}_2$ spin liquids.

Findings

Method successfully distinguishes different $ ext{Z}_2$ spin liquid states.

Applicable to projected wave functions on the kagome lattice.

Can classify and differentiate candidate states.

Abstract

In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected $\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of $\mathbb Z_2$ spin liquid states on the kagome lattice.