This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

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

The emergence of statistical mechanics for isolated classical systems comes about through
chaotic dynamics and ergodicity. Here we review how similar questions can be answered in …

We show that the combination of charge and dipole conservation—characteristic of fracton
systems—leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead …

The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe
observables in isolated integrable quantum systems after equilibration. Since then, the GGE …

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 …

We propose a general method to embed target states into the middle of the energy spectrum
of a many-body Hamiltonian as its energy eigenstates. Employing this method, we construct …

The relaxation of isolated quantum many-body systems is a major unsolved problem
connecting statistical and quantum physics. Studying such relaxation processes remains a …

We review the recent progress in the understanding of the relaxation of isolated near-
integrable quantum many-body systems. Focusing on prethermalization and universal …

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in
both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the …