The approach to thermal equilibrium, or thermalization, in isolated quantum systems is
among the most fundamental problems in statistical physics. Recent theoretical studies have …

This topical review article gives an overview of the interplay between quantum information
theory and thermodynamics of quantum systems. We focus on several trending topics …

We report universal statistical properties displayed by ensembles of pure states that
naturally emerge in quantum many-body systems. Specifically, two classes of state …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

How do closed quantum many-body systems driven out of equilibrium eventually achieve
equilibration? And how do these systems thermalize, given that they comprise so many …

Many-body localization is shown to suppress the imaginary parts of complex eigenenergies
for general non-Hermitian Hamiltonians having time-reversal symmetry. We demonstrate …

We construct a complete set of local integrals of motion that characterize the many-body
localized (MBL) phase. Our approach relies on the assumption that local perturbations act …

We discuss a method of numerically identifying exact energy eigenstates for a finite system,
whose form can then be obtained analytically. We demonstrate our method by identifying …

This Colloquium gives an overview of recent theoretical and experimental progress in the
area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus …

We ask whether the eigenstate thermalization hypothesis (ETH) is valid in a strong sense: in
the limit of an infinite system, every eigenstate is thermal. We examine expectation values of …