A journey into localization, integrability and thermalization

TL;DR

This paper explores many-body localization, ergodicity breaking, and thermalization in spin chains and random matrix models, introducing an exactly solvable Richardson model to study localized phases and analyzing thermalization properties.

Contribution

It introduces the Richardson model as an exactly solvable system for studying many-body localization and investigates thermalization in random matrix ensembles.

Findings

Localization transition observed in spin chains.

Richardson model effectively captures localized phases.

Eigenstate Thermalization Hypothesis validity analyzed.

Abstract

We present here the results obtained during my PhD work. We report the study of the many body localization transition in a spin chain and the breaking of ergodicity measured in terms of return probability in a state evolution. Moreover, we introduce the Richardson model, an exactly solvable model, that turns out to be suitable for investigating the many-body localized phase. Then we turn to the analysis of the quench problem in an ensemble of random matrices. We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis for the typical case, where the quench parameter explicitly breaks a Z_2 symmetry.