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Understanding how isolated quantum systems thermalize has recently gatheredrenewed interest almost 100 years after the first work by von Neumann, thanksto the experimental realizations of such systems. Experimental and numericalpieces of evidence imply that nonintegrability of the system plays an importantrole in thermalization. Nonintegrable systems that conserve energy alone areexpected to be effectively described by the (micro)canonical ensemble due tothe so-called eigenstate thermalization hypothesis (ETH) in the thermodynamiclimit. In contrast, it is expected that stationary states in integrable systemsare described not by the canonical ensemble but by the generalized Gibbsensemble (GGE) due to the existence of many nontrivial conserved quantities.  In this thesis, we study thermalization and its mechanism in nonintegrablesystems from two perspectives. We first study how well the ETH and itsfinite-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 withan extensive number of local symmetries.

Theoretical study on thermalization in isolated quantum systems