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.

arXiv comment10+epsilon pages, 4 figures

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• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Coupled Wire Models of Interacting Dirac Nodal Superconductors
• Twisted coupled wire model for a moiré sliding Luttinger liquid
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• Dihedral twist liquid models from emergent Majorana fermions
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• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires