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 …

We overview the concept of dynamical phase transitions (DPTs) in isolated quantum
systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized …

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 …

We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite
consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving …

A network is frustrated when competing interactions between nodes prevent each bond from
being satisfied. This compromise is central to the behaviour of many complex systems, from …

We review recent theoretical work on two closely related issues: excitation of an isolated
quantum condensed matter system driven adiabatically across a continuous quantum phase …

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 …

In this work, we describe in detail the chopped random basis (CRAB) optimal control
technique recently introduced to optimize time-dependent density matrix renormalization …

In this work we discuss the existence of time-translation symmetry breaking in a kicked
infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model …

A quantum simulator is a well-controlled quantum system that can follow the evolution of a
prescribed model whose behaviour may be difficult to determine. A good example is the …