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

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.