Aspects of Eigenstate Thermalization

For chaotic quantum many-body systems, the eigenstate thermalization hypothesis (ETH) posits that energy eigenstates contain the properties of equilibrium ensembles. Many subsequent devel- opments have demonstrated the centrality of random matrix theory and free probability to the ETH. This thesis focuses primarily on a version of the ETH known as ergodic bipartition (EB). The fundamental physical result of the EB is that the entanglement entropy of a subsystem is its thermodynamic entropy, or, more generally, that local thermodynamics of isolated quantum sys- tems are sourced in entanglement. I discuss two sets of results: (I) a diagrammatic calculus for the EB that supports a refined view of entanglement dynamics in chaotic quantum systems and (II) an application of the EB to systems with compact non-Abelian symmetries. In chapter 1, I aim to convince the reader why the ETH contains a profound insight into the thermodynamic limit, and in doing so, justify why it is worthy of study. I then put forth a mini- mally technical motivation for each of the two main chapters of the thesis. In chapter 2, I present the results of ref. [37]. First, we develop a unified diagrammatic approach to the EB and the ETH that systematically incorporates all corrections predicted by random matrix theory. We use this approach to review, and occasionally correct, previous literature on the EB. Then we demonstrate that universal state-based dynamics, including the universal dynamics of entanglement, are fully captured by our formalism. In chapter 3, I present the results of a yet-to-be-published manuscript. In this work, we extend the EB and the ETH to systems with symmetries given by general compact Lie groups, based on prior work studying the ETH in systems with SU(2) symmetry. We show that the ETH and EB hold in a symmetry-adapted way which introduces universal logarithmic subtrac- tions to thermodynamic entropy. General state and operator correlations are governed additionally by Clebsch–Gordan coefficients, which do not thermalize, but do strongly semiclassicalize. Thus, to compute entanglement entropy we produce a general semiclassical analysis of Clebsch–Gordan coefficients finding universal logarithmic additions to entanglement. In chapter 4, I discuss the outlook for research on the ETH and speculate where I feel the most important results remain to be discovered.

Name thesis:degree_name

Doctor of Philosophy

Discipline thesis:degree_discipline

Physics

Grantor

University of Houston

Year dc:date.issued

2026

Author dc:creator

• Jindal, Siddharth

Advisor dc:contributor.advisor

• Hosur, Pavan

Committee members dc:contributor.committeemember

• Bittner, Eric R.
• Vershynina, Anna
• Bellwied, Rene
• Mondaini, Rubem

• Quantum chaos
• Statistical mechanics
• Random matrix theory

Language dc:language.iso

English

Handle dc:identifier.uri

https://hdl.handle.net/10657/21494

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/21494