Projective symmetry group classification of chiral $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model

TL;DR

This paper classifies all symmetric and chiral $ ext{Z}_2$ quantum spin liquids on the pyrochlore lattice using projective symmetry group analysis, identifying 50 ans"atze and exploring their properties within the spin-$1/2$ XXZ model.

Contribution

It provides a comprehensive classification of $ ext{Z}_2$ spin liquids on the pyrochlore lattice, including new chiral states with unique flux properties.

Findings

Identified 50 independent $ ext{Z}_2$ spin liquid ans"atze.

Discovered four chiral spin liquids breaking screw symmetry.

Characterized flux patterns and symmetry properties of these states.

Abstract

We give a complete classification of fully symmetric as well as chiral $\mathbb{Z}_2$ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ans\"atze, including the 12 fully symmetric nearest-neighbor $\mathbb{Z}_2$ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ans\"atze by solving the mean-field equations for the spin-$1/2$ XXZ model near the antiferromagnetic Heisenberg point. We find four chiral spin liquids that break the screw symmetry of the lattice modulo time reversal symmetry. These states have a different symmetry than the previously studied monopole flux state and their unique characteristic is a $\frac{\pi}{3}$ flux enclosed by every rhombus of the lattice.