Hidden Classicality in a Driven-Dissipative Quantum Spin Model

There is renewed interest in the physics of the dissipative transverse-field Ising model, driven both by recent experiments on driven-dissipative atomic ensembles probing phase transitions [1,2] and by surprising theoretical predictions (e.g. time-crystalline phenomena [3]). It was recently discovered that a variant of this model is exactly solvable, even in regimes lacking any collective or permutational symmetry [4]. Here, we explore a surprising, exact connection between the dissipative steady state of this model (and its phase transition physics) and a fully classical stochastic model. We show how this effective classical model captures all properties of the non-equilibrium steady state, and even allows insights into dynamics. Our investigation opens a route to exact solutions for an even broader class of dissipative models.

[1] G. Ferioli et al, Nature Physics 19, 1345-1349 (2023)

[2] E.Y. Song et al, arXiv:2408.11086 (2024)

[3] F. Iemini et al, PRL 121, 035301 (2018)

[4] D. Roberts et al, PRL 131, 190403 (2023)