Entangling symmetry and topology in correlated electrons

Abstract

In this thesis, I study a class of exotic quantum matter named Symmetry-Protected Topological (SPT) phases. These are short-range-entangled quantum phases hosting non-trivial states on their boundaries. In the free-fermion limit, they are famously known as Topological Insulators (TI). Huge progress has been made recently in understanding SPT phases beyond free fermions. Here I will discuss three aspects of SPT phases in interacting systems, mostly in three dimensions: (1) Novel SPT phases could emerge in strongly correlated systems, with no non-interacting counterpart. In particular, I will discuss interaction-enabled electron topological insulators, including their classification, construction, characterization and realization. (2) When strong interactions are present, the surface of many SPT phases (including the familiar free fermion topological insulator) can be gapped without breaking any symmetry, at the expense of having intrinsic topological order on the surface. (3) Some topological phases that are non-trivial in the free fermion theory become trivial once strong interactions are introduced. The material of this thesis closely parallels that of Refs. [1, 2, 3, 4, 5, 6].