Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet

TL;DR

This paper investigates a spin-1 Heisenberg model on a square lattice, revealing a phase diagram with magnetic orders and a non-Abelian spin liquid, demonstrating coexistence of fractionalized excitations and magnetic order.

Contribution

It identifies a non-Abelian Moore-Read spin liquid phase coexisting with magnetic order in a simple spin-1 system, expanding understanding of quantum spin liquids.

Findings

Discovery of a non-Abelian Moore-Read spin liquid phase.

Coexistence of stripe magnetic order with the spin liquid.

Mapping of a comprehensive phase diagram including magnetic and spin liquid phases.

Abstract

We study the ground-state properties of a spin-1 Heisenberg model on a square lattice with the first- and second-nearest-neighbor antiferromagnetic couplings $J_1$ and $J_2$ and a three-spin scalar chirality term $J_\chi$. Using the density matrix renormalization group calculation, we map out a global phase diagram including various magnetic order phases and an emergent quantum spin liquid phase. The nature of the spin liquid is identified as a bosonic non-Abelian Moore-Read state from the fingerprint of the entanglement spectra and identification of a full set of topological sectors. We further unveil a stripe magnetic order coexisting with this spin liquid. Our results not only establish a rare example of non-Abelian spin liquids in simple spin systems but also demonstrate the coexistence of fractionalized excitations and magnetic order beyond mean-field descriptions.