A finite-momentum superfluid on a frustrated honeycomb lattice

We study finite-momentum superfluidity in a frustrated honeycomb Bose-Hubbard model that exhibits a dispersion minimum on a closed curve - a "moat". Boson condensation on any point of the moat minimum leads to a novel smectic superfluid state with fluctuations qualitatively stronger than in conventional superfluids. We compute a variety of its properties, including condensate depletion, equation of state, momentum distribution, and structure function. While stable at zero temperature, in a continuum approximation such superfluid exhibits a 3d quasi-long-range order at any nonzero temperature. Quantum order-by-disorder at low energies manifests lattice-broken rotational symmetry and asymptotically leads to a crossover to a conventional long-range ordered superfluid state. We complement the microscopic lattice analysis with a field theory description for such nonzero momentum superfluids, finding a reassuring agreement and allowing us to confront general questions about such phenomena.