Quantum circuits—built from local unitary gates and local measurements—are a new
playground for quantum many-body physics and a tractable setting to explore universal …

Recent years have witnessed an explosion of interest in quantum devices for the production,
storage, and transfer of energy. This Colloquium concentrates on the field of quantum …

The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

Weakly interacting quasiparticles play a central role in the low-energy description of many
phases of quantum matter. At higher energies, however, quasiparticles cease to be well …

The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in
the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of …

Quantum many-body systems display rich phase structure in their low-temperature
equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was …

Recent years have seen remarkable development in open quantum systems effectively
described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological …

The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …