Two dimensional spin liquids with $\mathbb{Z}_2$ topological order in an array of quantum wires

TL;DR

This paper constructs a time-reversal symmetric two-dimensional $ ext{Z}_2$ spin liquid using quantum wire arrays, identifying anyons as kinks in a Luttinger liquid and exploring their properties, along with a fractionalized Fermi-liquid extension.

Contribution

It introduces a novel construction of a $ ext{Z}_2$ spin liquid in 2D with explicit anyon descriptions and a coupled fractionalized Fermi-liquid phase.

Findings

Identification of anyons as kinks in Luttinger liquids

Explicit mutual statistics of quasiparticles computed

Construction of a fractionalized Fermi-liquid (FL*) phase

Abstract

Insulating $\mathbb{Z}_2$ spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground state degeneracies on manifolds with non-trivial topology. In this paper, we construct a time-reversal symmetric $\mathbb{Z}_2$ spin liquid in two spatial dimensions using an array of quantum wires. We identify the anyons as kinks in the appropriate Luttinger-liquid description, compute their mutual statistics and construct local operators that transport these quasiparticles. We also present a construction of a fractionalized Fermi-liquid (FL*) by coupling the spin sector of the $\mathbb{Z}_2$ spin-liquid to a Fermi-liquid via a Kondo-like coupling.