Physical interactions in quantum many-body systems are typically local: Individual
constituents interact mainly with their few nearest neighbors. This locality of interactions is …

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 …

An understanding of the temporal evolution of isolated many-body quantum systems has
long been elusive. Recently, meaningful experimental studies, of the problem have become …

We introduce and explore a one-dimensional “hybrid” quantum circuit model consisting of
both unitary gates and projective measurements. While the unitary gates are drawn from a …

We review the conformal field theory approach to entanglement entropy in 1+ 1 dimensions.
We show how to apply these methods to the calculation of the entanglement entropy of a …

In this paper we continue to explore “hybrid” quantum circuit models in one-dimension with
both unitary and measurement gates, focusing on the entanglement properties of wave …

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ
spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state …

A bstract We study chaos and scrambling in unitary channels by considering their
entanglement properties as states. Using out-of-time-order correlation functions to diagnose …

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