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Quantum States: With a View Toward Homological Algebra


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


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Stabilizer codes, anyons, KMS states, SPT phases, invertible states, linear response
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2023.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Thesis Committee:
  • Marcolli, Matilde (chair)
  • Chen, Xie
  • Motrunich, Olexei I.
  • Kapustin, Anton N.
Defense Date:16 May 2023
Record Number:CaltechTHESIS:05172023-003322589
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter II. adapted for Chapter III. adapted for Chapter IV.
Yang, Bowen0000-0003-4778-831X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15183
Deposited By: Bowen Yang
Deposited On:02 Jun 2023 23:12
Last Modified:16 Jun 2023 18:13

Thesis Files

[img] PDF (Final thesis file) - Final Version
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