Multipole Symmetries and Many Body Physics

Abstract

This thesis studies the many body physics of systems with multipolar conservation laws --- systems which conserve both a total charge and various multipole moments thereof. These conservation laws place constraints on the way in which particles can move, and carry important ramifications for both quantum ground states and non-equilibrium dynamics. Particular emphasis is placed on Hubbard models with dipole moment conservation, which are of special interest due to their ability to be experimentally realized in strongly tilted optical lattices. The bosonic versions of these models are shown to possess unusual insulating Bose-Einstein condensates in their ground states, accompanied by unconventional patterns of spontaneous symmetry breaking. The fermionic versions on the other hand are shown to host exotic non-Fermi liquids. We also report progress on understanding the ramifications that multipole conservation has for diffusion, showing that it leads to unusually large dynamical exponents and exponentially localized disorder-free steady states.