# Theoretical study on thermalization in isolated quantum systems

## TL;DR

This paper provides a theoretical analysis of thermalization mechanisms in isolated quantum systems, focusing on the eigenstate thermalization hypothesis and the emergence of generalized Gibbs ensembles in nonintegrable models.

## Contribution

It offers a theoretical investigation into how ETH and GGE describe thermalization, including predictions from random matrix theory and the role of local symmetries.

## Key findings

- ETH predictions align with RMT in finite-size systems
- GGE emerges in nonintegrable systems with local symmetries
- Finite-size corrections to ETH are characterized

## Abstract

Understanding how isolated quantum systems thermalize has recently gathered renewed interest almost 100 years after the first work by von Neumann, thanks to the experimental realizations of such systems. Experimental and numerical pieces of evidence imply that nonintegrability of the system plays an important role in thermalization. Nonintegrable systems that conserve energy alone are expected to be effectively described by the (micro)canonical ensemble due to the so-called eigenstate thermalization hypothesis (ETH) in the thermodynamic limit. In contrast, it is expected that stationary states in integrable systems are described not by the canonical ensemble but by the generalized Gibbs ensemble (GGE) due to the existence of many nontrivial conserved quantities. In this thesis, we study thermalization and its mechanism in nonintegrable systems from two perspectives. We first study how well the ETH and its finite-size corrections can be predicted by random matrix theory (RMT). Next, we present our study on the emergence of the GGE in a nonintegrable system with an extensive number of local symmetries.