Spinon quantum spin Hall state in the kagome antiferromagnet with a Dzyaloshinskii-Moriya interaction

TL;DR

This paper predicts a novel gapped quantum spin liquid state with topological order and spinon edge states in a kagome antiferromagnet with Dzyaloshinskii-Moriya interaction, resembling a quantum spin Hall insulator.

Contribution

It introduces a new spinon quantum spin Hall state in a kagome antiferromagnet, characterized by topological order and spinon edge states, arising from a topological transition induced by anisotropic interactions.

Findings

Identifies a gapped quantum spin liquid with topological degeneracy

Shows the state has spinon edge states with opposite chiralities

Demonstrates the state as a time-reversal symmetric topological insulator

Abstract

We investigate the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on kagome lattice, making use of the variational Monte Carlo technique. An exotic quantum spin state is found to arise from a melting of the $\boldsymbol{Q} = 0$ long-range magnetic order by a topological transition, when a small anisotropic third nearest-neighbor antiferromagnetic Heisenberg interaction is turned on. This novel state is a gapped quantum spin liquid, characterized by a topological order with ground-state degeneracy $n_g = 4$ and topological entanglement entropy $\gamma = \ln 2$, suggesting it is an Abelian topological phase. Furthermore, the Chern numbers of the spin-up (-down) spinon occupied bands of this state are $C_{\uparrow \downarrow} = \pm 1$, respectively. From this perspective, this state is also a time-reversal symmetric (total Chern number $C_{total} = 0$) topological insulator with spinons as the chiral edge states, which carry opposite spin and move in the opposite direction. It is analogous to the quantum spin Hall state but the spin current is carried by deconfined spinons in a quantum spin liquid, so is dubbed as the spinon quantum spin Hall state.