Model of spin liquids with and without time-reversal symmetry

TL;DR

This paper investigates a (2+1)D spin liquid model realized by coupled spin ladders, revealing stable Abelian and non-Abelian phases, including a gapless non-Abelian spin liquid, with implications for symmetry-breaking and phase transitions.

Contribution

It introduces a lattice realization of a (2+1)D spin liquid model with Majorana fields, analyzing phases with and without time-reversal symmetry using mean-field theory.

Findings

Identification of stable Abelian and non-Abelian spin liquid phases.

Discovery of a gapless non-Abelian spin liquid regime.

Observation of phase transitions involving symmetry breaking.

Abstract

We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current interactions. The model is shown to have a lattice realization in an array of two-leg quantum spin-1/2 ladders. We study the model both in the presence and absence of time-reversal symmetry, within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime where a non-chiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2+1)-dimensional spacetime, much as those appearing in the Kitaev honeycomb model, but here emerging in a model of coupled spin ladders that does not break SU(2) spin-rotation symmetry.