Chiral bosonic Mott insulator on the frustrated triangular lattice

We study the superfluid and insulating phases of interacting bosons on the triangular lattice with an inverted dispersion, corresponding to frustrated hopping between sites. The resulting single-particle dispersion has multiple minima at nonzero wave vectors in momentum space, in contrast to the unique zero-wave-vector minimum of the unfrustrated problem. As a consequence, the superfluid phase is unstable against developing additional chiral order that breaks time-reversal (T) and parity (P) symmetries by forming a condensate at nonzero wave vector. We demonstrate that the loss of superfluidity can lead to an even more exotic phase, the chiral Mott insulator, with nontrivial current order that breaks T, P. These results are obtained via variational estimates, as well as a combination of bosonization and density-matrix renormalization group of triangular ladders, which, taken together, permit a fairly complete characterization of the phase diagram. We discuss the relevance of these phases to optical lattice experiments, as well as signatures of chiral symmetry breaking in time-of-flight images.