Structure of Entanglement in Fracton Phases of Matter

Citation

Shirley, Wilbur Eric (2022) Structure of Entanglement in Fracton Phases of Matter. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7b2c-2e06. https://resolver.caltech.edu/CaltechTHESIS:05272022-220331463

Abstract

This thesis discusses recent contributions to the theory of gapped fracton phases of matter, utilizing exactly solvable Hamiltonian models as the primary tool of study. A large component of the work revolves around the notion of a foliation structure, which is a defining feature of the long-range entanglement in certain gapped fracton states. We introduce this concept, identify its presence in a handful of prominent fracton models, and explore its consequences in terms of entanglement entropy and fractional excitations. A second major theme of the thesis is the characterization of gapped fracton states via emergent gauge theories based on discrete subsystem symmetries. We introduce a variety of novel fractonic gauge theories including twisted and fermionic variants, identify their emergence in a bevy of well-known models, and classify them with the use of novel topological invariants. We also establish a link between subsystem symmetry and entanglement renormalization group flow in fractal spin liquids.

Thesis Files