Correlated phases of bosons in tilted, frustrated lattices

TL;DR

This paper explores various correlated quantum phases of bosons in tilted, frustrated lattices, revealing novel density wave, superfluid, and quantum liquid states through theoretical models and exact solutions.

Contribution

It extends previous work to multiple 2D lattice geometries and tilt directions, identifying new phases and the necessity of three-body interactions for stability.

Findings

Discovery of Ising density wave order in certain lattice configurations.

Identification of superfluidity transverse to the tilt direction.

Existence of a quantum liquid state with no broken symmetry, supported by an exact solution.

Abstract

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 non-trivial entanglement of pseudospin degrees of freedom encoded in the boson density. We extend a previous study (arXiv:cond-mat/0205169) of cubic lattices to a variety of lattices and tilt directions in 2 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, with superfluidity transverse to the tilt direction, and a quantum liquid state with no broken symmetry. The existence of the quantum liquids 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.