We explore the evolution of a strongly interacting dissipative quantum Ising spin chain that is driven by a slowly varying time-dependent transverse field. This system possesses an extensive number of instantaneous (adiabatic) stationary states which are coupled through non-adiabatic transitions. We analytically calculate the generator of the ensuing slow dynamics and analyze the creation of coherences through non-adiabatic processes. For a certain choice of the transverse field shape, we show that the system solely undergoes transitions among classical basis states after each pulse. The concatenation of many of such pulses leads to an evolution of the spin chain under a many-body dynamics that features kinetic constraints. Our setting not only allows for a quantitative investigation of adiabatic theorems and non-adiabatic corrections in a many-body scenario. It also directly connects to many-body systems in the focus of current research, such as ensembles of interacting Rydberg atoms which are resonantly excited by a slowly varying laser pulse and subject to dephasing noise.
Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master equation, and generically applies to regimes beyond the reach of conventional spin-wave theories, including short-range interactions and local quantum jumps, enabling the efficient simulation of large-scale interacting spins. We illustrate the versatility of our framework by studying a variable-range driven-dissipative Ising model on a 2D lattice. When the dissipation acts along the drive axis, we find a continuous phase transition breaking the
Z2 symmetry, and demonstrate that the interaction range, when tuned from fully-connected to nearest-neighbour, profoundly alters the universality class of the criticality. With the dissipation along the interaction axis, we show the emergence of a first-order transition. Demonstrated with both state-diffusion and quantum-jump types of trajectory dynamics, our framework provides a powerful toolbox for the efficient semiclassical description of non-equilibrium dynamics and many-body phases in spin systems.