Nonthermal phases of driven matter

Over the past years a series of works has greatly advanced our understanding of how nonthermal drives and baths affect the collective behavior of many-body systems, from open quantum systems to active matter. In particular, intense laser driving can stabilize ordered phases in materials, including superconducting and ferromagnetic states, at bath temperatures where equilibrium would not allow such order. This raises a general question: What kind of many-body steady states that cannot exist in equilibrium, i.e. as a minimum of a free energy, are possible, what are their macroscopic properties and what mechanism can stabilize them? We develop the open-system effective field theory for phases with an O(N) order parameter and show that it admits genuinely nonthermal phases with long-range order evolving on a limit cycle, a behavior ruled out in equilibrium. Unlike equilibrium phases, their stability is controlled not by free-energy curvature but by the competition between drive and dissipation. We present analytical and numerical evidence that rapid parametric drives that are oftentimes used to model light-driven materials can stabilize these phases of matter. The theory predicts a new nonthermal universality class, fluctuation-induced first-order transitions into the limit-cycle phase. For low symmetry systems the Goldstone dynamics within the limit cycle lays in the Kardar-Parisi-Zhang (KPZ) universality class. We predict novel universal scaling laws for larger symmetry spaces. Related KPZ-Goldstone physics has recently been observed in a two-dimensional driven-dissipative exciton-polariton condensate.