# Multistability of Driven-Dissipative Quantum Spins

## TL;DR

This paper investigates the multistability phenomena in driven-dissipative quantum spin lattices, revealing how correlations influence steady states and proposing a scheme to go beyond meanfield approximations, with implications for experiments.

## Contribution

It introduces an efficient method to include correlations beyond meanfield and demonstrates the impact of correlations on multistability in quantum spin models.

## Key findings

- Correlations eliminate meanfield bistability in 1D, leading to a unique steady state.
- Multistability persists in 2D and higher dimensions when considering the thermodynamic limit.
- Parameter variations cause jumps between steady states with critical slowing down.

## Abstract

We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the meanfield limit of these models manifests multistable parameter regions of 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, provided the thermodynamic limit of an infinitely large lattice is taken first with respect to the long time limit. Variation of the system parameters results in 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.