Novel Quantum States of Bosons in Moat Bands

We study hard-core bosons on a class of frustrated lattices with the lowest Bloch band having a degenerate minimum along a closed contour in the reciprocal space -- the Moat. We suggest that the ground state of the system is given by non-condensed state, which may be viewed as a state of fermions subject to Chern-Simons gauge field. At fixed density of bosons, such a state exhibits domains of incompressible liquids. Their fixed densities are given by fractions of the reciprocal area enclosed by the minimal energy contour.