Spontaneous formation of a nonuniform chiral spin liquid in a moat-band lattice

A number of lattices exhibit moatlike 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 the s=1/2  XY model at a zero magnetic field, while the absence of condensation translates into the absence of magnetic order in the XY plane. Here, we show that the ground state breaks 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.