Understanding, constructing, and probing highly-entangled phases of quantum matter

Abstract

In this thesis, I explore three classes of quantum phases of matter that cannot be understood purely on the basis of symmetry, and can be regarded (to varying degrees) as having highly-entangled ground-states. The first Part describes topological superconductors with non-Abelian defects, and develops realistic routes to constructing these exotic superconductors from more elementary materials. Particular attention is payed to practical issues such as disorder. The second Part examines the role of interactions in electron topological insulators (TIs). Non-perturbative definitions of the familiar topological band-insulator are given, and new strongly-correlated TIs with no band-structure analogs are identified. The last Part turns exotic gapless phases without quasi-particle excitations, focusing on topics related to recently discovered quantum spin-liquid (QSL) materials. The possibility of a gapless QSL in the vicinity of the metal-insulator transition in doped semiconductors is explored, and optical conductivity is developed as an experimental tool to examine the nature of the QSL candidate Herbertsmithite. The material of this thesis is closely parallels that of Refs [1, 2, 3, 4, 5, 7,8, 9,10, 11].