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 …

This Colloquium describes a new paradigm for creating strong quantum interactions of light
and matter by way of single atoms and photons in nanoscopic lattices. Beyond the …

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct
approach to decomposing the exponential of a sum of operators. Despite significant effort …

We show that the time-dependent variational principle provides a unifying framework for
time-evolution methods and optimization methods in the context of matrix product states. In …

The maximum speed with which information can propagate in a quantum many-body system
directly affects how quickly disparate parts of the system can become correlated,,, and how …

Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

Quantum state tomography is the standard technique for estimating the quantum state of
small systems. But its application to larger systems soon becomes impractical as the …

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting
quantum spin models. Effective spins are represented by appropriate internal energy levels …

We show that exciton-type transport in certain materials can be dramatically modified by
their inclusion in an optical cavity: the modification of the electromagnetic vacuum mode …

We study scrambling in connection with multipartite entanglement dynamics in regular and
chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For …