From Effective Temperature to Non-Boltzmann State Selection in Driven-Dissipative Quantum Criticality

Abstract:Whether a nonequilibrium quantum-critical steady state can be described by an effective temperature remains an open question. We address it in a voltage-biased electronic Lipkin--Meshkov--Glick model, a minimal driven-dissipative model of a collective spin coupled to metallic leads. A controlled large-$N$ treatment reveals an overdamped open quantum-critical regime distinct from the closed model. The surrounding quantum critical fan, organized by temperature and voltage, is explored and fluctuations are found to be governed by an effective temperature $T_{\rm eff}$. At strong bias, the transition becomes first-order through a tricritical point. Remarkably, the same $T_{\rm eff}$ governs the strongly driven regime, but now varies across the entire order-parameter landscape. The steady state is therefore selected by a non-Boltzmann rule, shifting the first-order transition away from the equal-depth point of a deterministic potential. Driven criticality thus remains organized by an effective temperature while revealing non-thermal state selection.

Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2609.25242 [cond-mat.str-el]

(or arXiv:2609.25242v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2609.25242 arXiv-issued DOI via DataCite (pending registration)