Beatriz Olmos

Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems like arrays of Rydberg atoms, atom-cavity systems or trapped ion crystals. For theoretical analysis the mean-field (MF) ansatz is routinely applied. However, besides special cases of all-to-all or strong long range interactions, the MF ansatz provides only approximate results. Here we present a systematic correction to MF theory based on diagrammatic perturbation theory for quantum spin correlators in thermal equilibrium. Our analytic results are universally applicable for any lattice geometry and spin-length S. We provide pre-computed and easy-to-use building blocks for Ising, Heisenberg and transverse field Ising models in the symmetry-unbroken regime. We showcase the quality and simplicity of the method by computing magnetic phase boundaries and excitations gaps. We also treat the Dicke-Ising model of ground-state superradiance where we show that corrections to the MF phase boundary vanish.

We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field and dissipation rate, we identify a first order dynamical phase transition between active and inactive {\em dynamical phases}. We demonstrate that dynamical phase-coexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity, and the longitudinal magnetization that serves as static order parameter. The system we consider can be implemented in current experiments with Rydberg atoms and trapped ions.