Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices

TL;DR

This paper demonstrates that in moat-band lattices populated with hard-core bosons, the ground state forms a non-uniform chiral spin liquid that breaks time-reversal and inversion symmetries, featuring a bulk gap and chiral edge states.

Contribution

It introduces an analytical theory explaining the spontaneous formation of a chiral spin liquid in moat-band lattices, connecting to numerical results and experimental realizations.

Findings

Ground state breaks time-reversal and inversion symmetries.

State has a bulk gap and chiral gapless edge excitations.

Applicable to cold atom experiments in optical lattices.

Abstract

A number of lattices exhibit moat-like band structures, i.e. a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to $s=1/2$ XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.