1:00–2:00 pm
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Please Join us:
Kyle Kawagoe's PhD Thesis Defense
Tuesday, July 5 2022 at 1:00 PM CDT
MICROSCOPIC DEFINITIONS OF TOPOLOGICAL DATA
Condensed matter physics rests its foundation on the notion of phases of matter with universal properties. As it is not possible to understand the detailed motions of large collections of particles by tracking them individually, we must rely on the fact that, much of the time, these details are irrelevant to a comprehensive understanding of a macroscopic system. Rather, we must understand the collective behavior of materials via a small set of quantities which summarize this information. For topological phases of matter, which are realized in quantum many-body systems, we can understand their most basic properties from information called ``topological data." This topological data describes the phase of matter of these systems and carries with it a broad array of information about their behavior. Previously, the nature of this data was broadly understood, but in most cases was lacking a concrete interpretation in terms of the microscopic details of these systems.
In this talk, I will resolve this issue by giving concrete definitions of the topological data in terms of a small number of microscopic properties of these systems. These definitions serve not only as a tool to analyze these theories, but also bridge a conceptual gap between the abstract mathematical understanding of these phases of matter with the concrete physical models that physicists study. I will discuss two types of (2+1)D topological phases of matter: intrinsic topological phases (exemplified by fractional quantum Hall states) and symmetry protected topological phases (exemplified by topological insulators). For intrinsic topological order, I will describe data which can be derived from properties of their anyons. For symmetry protected topological phases, I will show how to extract the data from the properties of their edge modes.
Committee Members:
(Chair): Michael Levin
Dam T. Son
Arvind Murugan
Jonathan Simon
Kyle will be heading to The Ohio State University as a Postdoctoral Scholar in the Physics Department, advised by Brian Skinner and Yuan-Ming Lu, and as a PhD Lecturer in the Mathematics Department, teaching and doing research with David Penneys. In these dual roles, he will continue bridging the gap between the physical and mathematical perspectives of condensed matter physics and will remain dedicated to his passion for pedagogy.