The recently engineered frustrated optical lattices are remarkable for their capacity to explore physics that may not be revealed in any other way. Examples include lattices having moatlike band structures, i.e., a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone.
It is entirely the effect of correlations which lifts this degeneracy and leads to an amazing variety of completely new quantum many-body states. 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.
In this talk I will argue that the frustration in such lattices stabilizes a variety of novel spin liquid phases including a composite fermion state and a chiral spin liquid. These are topologically nontrivial ground states, having 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.