Two-dimensional spin liquids with Z[subscript 2] topological order in an array of quantum wires

Abstract

Insulating Z[subscript 2] spin liquids are a phase of matter with bulk anyonic quasiparticle excitations and ground-state degeneracies on manifolds with nontrivial topology. We construct a time-reversal symmetric Z[subscript 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 Z[subscript 2] spin liquid to a Fermi liquid via a Kondo-like coupling.