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 …

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 …

Experimental advances have allowed for the exploration of nearly isolated quantum many-
body systems whose coupling to an external bath is very weak. A particularly interesting …

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 …

Simulating the real-time evolution of quantum spin systems far out of equilibrium poses a
major theoretical challenge, especially in more than one dimension. We experimentally …

The many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

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 …

Certain disorder-free Hamiltonians can be nonergodic due to a strong fragmentation of the
Hilbert space into disconnected sectors. Here, we characterize such systems by introducing …

Eigenstate thermalization is widely accepted as the mechanism behind thermalization in
generic isolated quantum systems. Using the example of a single magnetic defect …