Exact Solution of the Infinite-Range Dissipative Transverse-Field Ising Model

The dissipative variant of the Ising model in a transverse field is one of the most important models in the analysis of open quantum many-body systems, due to its paradigmatic character for understanding driven-dissipative quantum phase transitions, as well as its relevance in modeling diverse experimental platforms in atomic physics and quantum simulation. Here, we present an exact solution for the steady state of the transverse-field Ising model in the limit of infinite-range interactions, with local dissipation and inhomogeneous transverse fields. Our solution holds despite the lack of any collective spin symmetry or even permutation symmetry. It allows us to investigate first- and second-order dissipative phase transitions, driven-dissipative criticality, and captures the emergence of a surprising "spin blockade" phenomenon. The ability of the solution to describe spatially varying local fields provides a new tool to study disordered open quantum systems in regimes that would be extremely difficult to treat with numerical methods.