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Phase transitions are ubiquitous in nature. For equilibrium cases, the celebrated Landau theory has provided great success in describing these phenomena on general grounds. Even for nonequilibrium transitions such as optical bistability, flocking transition, and directed percolation, one can often define a Landau’s free energy in a phenomenological way to successfully describe the transition at a meanfield level. In such cases, the nonequilibrium effect is present only through the noise-activated spatial-temporal fluctuations that break the fluctuation-dissipation theorem.

Here, by generalizing the Ginzburg-Landau theory to be applicable to driven systems, we introduce a novel class of nonequilibrium phase transitions [1-2] and critical phenomena [3] that does not fall into this class. Remarkably, the discovered phase transition is controlled by spectral singularity called the exceptional points that can only occur by breaking the detailed balance and therefore has no equilibrium counterparts. The emergent collective phenomena range from active time (quasi)crystals to exceptional point enforced pattern formation, hysteresis, to anomalous critical phenomena that exhibit anomalously large phase fluctuations (that diverge at d≤4) and enhanced many-body effects (that is relevant at d<8) [3]. The inherent ingredient to these is the non-reciprocal coupling between the collective modes that arise due to the drive and dissipation.

We demonstrate the emergence of these phenomena in a broad class of many-body interacting nonequilibrium systems both in quantum and classical amatter. Examples include driven quantum systems such as exciton-polariton condensates and BECs in a double-well potential and (classical) active matter where the different groups of agents are non-reciprocally interacting. Notably, our theory [2] provided the first explanation for the discontinuous transitions observed in many polariton experiments [4] and some viscous fingering experiments [5]. 

Our works lay the foundation of the general theory of critical phenomena in systems whose dynamics are not governed by an optimization principle.

[1]  M. Fruchart*, R. Hanai*, P. B. Littlewood, and V. Vitelli, Nature 592, 363 (2021).

[2]  R. Hanai, A. Edelman, Y. Ohashi, and P. B. Littlewood, Phys. Rev. Lett. 122, 185301 (2019).

[3]  R. Hanai and P. B. Littlewood, Phys. Rev. Res. 2, 033018 (2020).

[4]  See e.g., J. Tempel, et al., Phys. Rev. B 85, 075318 (2012).

[5] L. Pan, and J. R. de Bruyn, Phys. Rev. E 49, 483 (1994).

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