The Death of Quasiparticles: Strongly Interacting Gapless Phases with Fermi Surfaces and Fractional Statistics

Abstract

The emergence of quasiparticles at low temperature provides a powerful organizing principle for many quantum phases of matter, ranging from conventional magnets and superconductors to exotic insulators with topological order. In this thesis, I describe my research in gapless quantum phases in which the framework of quasiparticles breaks down. The main characters are two categories of gapless phases that feature the interplay between strong interactions and two additional ingredients – Fermi surfaces and fractional statistics. Chapter 2 through Chapter 5 focus on strongly interacting metals with Fermi surfaces. The most salient examples are a class of Hertz-Millis models describing the onset of spontaneous symmetry breaking in a metallic environment. At the quantum critical point, gapless order parameter fluctuations destroy quasiparticles living on the Fermi surface, giving rise to a strongly coupled non-Fermi liquid metal. A key result of these chapters is the identification of an infinite-dimensional symmetry that survives in these non-Fermi liquid metals despite the death of quasiparticles. This infinite-dimensional symmetry and its quantum anomaly lead to a series of non-perturbative results on thermodynamics and transport, which are confirmed by perturbative diagrammatic calculations in special examples. Chapter 6 through Chapter 8 explore quantum phases in which anyonic quasiparticles with fractional statistics play an essential role. When parameters in the system are tuned to close the anyon energy gaps, the original anyons lose their coherence and a variety of novel phases emerge. A highlight in this direction is a new mechanism for topological superconductivity in itinerant abelian and non-abelian anyon fluids, which could make contact with experiments on doped fractional quantum anomalous Hall states in the near future.