Young Jeremy T, Gorshkov Alexey V, Foss-Feig Michael, Maghrebi Mohammad F
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev X. 2020;10(1). doi: 10.1103/physrevx.10.011039.
Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) symmetry. However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a symmetry. Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
驱动耗散系统有望产生其平衡态对应物中不存在的非平衡现象。然而，尽管这些系统中的相变起源于非平衡态，但通常表现出有效的经典平衡行为。在本文中，我们表明此类系统中的多临界点会导致丰富且真正的非平衡行为。具体而言，我们研究了一个相互作用玻色子的驱动耗散模型，该模型具有两个不同的相变：一个是从高密度相到低密度相——类似于液 - 气转变——另一个是到反铁磁相。每个相变都由具有（涌现或微观）对称性的伊辛普适类来描述。然而，它们在一个多临界点合并，产生了一个由一种对称性描述的类似伊辛序参量耦合的非平衡模型。使用动态重整化群方法，我们表明出现了一对非平衡不动点（NEFP），它们支配着系统的长程临界行为。我们阐明了这些NEFP的各种奇异特征。特别是，我们表明临界时的一般连续尺度不变性会简化为离散尺度不变性。这进一步导致复数值的临界指数和螺旋状的相边界，并且即使接近相变也伴随着一个复李沃利间隙。作为NEFP非平衡性质的直接证据，我们表明在所有尺度上涨落耗散关系都被违反，导致有效温度在越来越长的波长下变得“越来越热”。最后，我们认为这种非平衡行为可以在具有交叉克尔非线性的腔阵列中观察到。
