Projective symmetry group classification of chiral spin liquids

TL;DR

This paper extends the projective symmetry group classification to chiral spin liquids, providing a systematic framework for their analysis on triangular and kagome lattices, including construction of Hamiltonians and wave functions.

Contribution

It introduces a generalized PSG classification method for chiral quantum spin liquids, expanding the understanding of their symmetry properties and possible phases.

Findings

Classified chiral $ ext{Z}_2$ spin liquids on triangular and kagome lattices.

Provided explicit construction methods for Hamiltonians and wave functions.

Analyzed static spin structure factors and symmetry constraints.

Abstract

We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then introduce a systematic generalization of the approach for symmetric $\mathbb{Z}_2$ quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral $\mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.