Quantum States: With a View Toward Homological Algebra

Author: Yang, Bowen

Year: 2023

Degree: Dissertation (Ph.D.)

Advisor: Kapustin, Anton N.

Committee Members: Marcolli, Matilde; Chen, Xie; Motrunich, Olexei I.; Kapustin, Anton N.

Option: Mathematics

DOI: 10.7907/fm81-v416

Abstract

The thesis comprises three papers covering different topics in quantum many-body physics. The first paper examines translationally invariant Pauli stabilizer codes, introducing invariants called charge modules and discussing their properties. The second paper explores invertible (G-invariant) states of 1D bosonic quantum lattice systems (or spin chains), demonstrating a full classification using group cohomology. The third paper analyzes the relation between ordinary correlators and Kubo's canonical correlators for thermal states of systems with short-range interactions. Overall, the thesis highlights the power of mathematics, especially homological methods, in understanding quantum states.

Files