Quantum States: With a View Toward Homological Algebra

Citation

Yang, Bowen (2023) Quantum States: With a View Toward Homological Algebra. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/fm81-v416. https://resolver.caltech.edu/CaltechTHESIS:05172023-003322589

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.

Thesis Files