Quantum liquids in dipole preserving Hubbard models.

Quantum liquids, states which do not have any ordering even at low temperatures, are usually obtained due to the frustration, for instance the quantum spin liquids.Another approach for generating these featureless states is to impose symmetries based on conservation laws in the model, a minimal one being the dipole conservation symmetry. There is a growing use of such symmetry imposed models as they can be realized by considering ultracold atoms in optical lattices with a tilted potential gradient. In this work, we discuss the incompressible quantum liquids in such dipole preserving Hubbard models. We demonstrate that the fluctuations in the center of mass, both in equilibrium and dynamics, characterize these quantum phases. We also discuss the connection of these models with the strongly correlated quantum Hall models.