Publication : t19/059

Abstract:
We study the dynamics of coupled quantum spins one-half on a lattice with nearest-neighbour "XY" (flip-flop) interactions, driven by external fields and subject to dissipation. The meanfield limit of the model manifests bistable parameter regions of two coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to meanfield by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product-operators in one- and two-dimensional lattices. Correlations are shown to wash the meanfield bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible in the thermodynamic limit. It is accompanied by jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics.

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