Correlated phases of bosons in tilted frustrated lattices

We study the "tilting" of Mott insulators of bosons into metastable states. These are described by Hamiltonians acting on resonant subspaces and have rich possibilities for correlated phases with nontrivial entanglement of pseudospin degrees of freedom encoded in the boson density. We extend a previous study [S. Sachdev, K. Sengupta, and S. M. Girvin, Phys. Rev. B 66, 075128 (2002)] of cubic lattices to a variety of lattices and tilt directions in two dimensions: square, decorated square, triangular, and kagome. For certain configurations three-body interactions are necessary to ensure that the energy of the effective resonant subspace is bounded from below. We find quantum phases with Ising density wave order and with superfluidity transverse to the tilt direction, and a quantum liquid state with no broken symmetry. The existence of the quantum liquid state is shown by an exact solution for a particular correlated boson model. We also find cases for which the resonant subspace is described by effective quantum dimer models.