Strongly Correlated Electronic Matter: Phases and their Transport

Abstract

This thesis surveys the research in strongly correlated matter that I have done over the course of my PhD. It can broadly be divided into two categories: phases of matter and their transport. My research into phases of matter has been concerned with the low energy properties of interacting electrons at fractional filling of an underlying lattice. I, along with collaborators, have shown that it is possible to have a continuous quantum phase transition between a metal and a generalized Wigner crystal that breaks the translation symmetry of the lattice. In a subsequent work we were able to support this with an exact bosonization treatment in the quasi-one dimensional setting. Finally, we have recently considered the possibility of an intervening topological phase where a gap opens, but translation symmetry remains unbroken. In doing so we formalized the concept of a “minimal” topological order and proved a number of results about these. My research into transport in strongly correlated systems involved: proposing an alternative explanation for magnetoresistance curves in a cuprate metal, and proposing a diagnostic of Hall viscosity in rotating Bose Einstein condensates using vortex dynamics.