Scaling properties of models of nonequilibrium phenomena

Baoquan Feng, Shuai Yin, Fan Zhong

A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large class of nonequilibrium systems. For such a manifestly nonlinear nonequilibrium strongly fluctuating system, we show that there exists universal nonequilibrium critical behavior that is incredibly well described by its equilibrium critical properties. A dynamic renormalization-group theory is developed to account for the behavior. The weak driving may give rise to several time scales depending on its form and thus rich nonequilibrium phenomena of various regimes and their crossovers, negative susceptibilities, as well as a violation of fluctuation-dissipation theorem and hysteresis. An initial condition that can be in either equilibrium or nonequilibrium but has longer correlations than the driving scales also results in a unique regime and complicates the situation. The implication of the results on measurement is also discussed. The theory may shed light on the study of other nonequilibrium systems and even nonlinear science.

Robin B. Stinchcombe, T. Hanney

Ming-Bao Yu

Kenji Harada

Using a tensor renormalization group method with oblique projectors for an anisotropic tensor network, we confirm that the rescaled spectrum of transfer matrices at nonequilibrium critical points in the (1+1)-dimensional directed percolation, a canonical model of nonequilibrium critical phenomena, is scale-invariant and its structure is universal.

Wilhelm Brenig

Yu-Rong Shu, Shuai Yin

Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical points (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J\text{\ensuremath{-}}{Q}_{3}$ model. In this paper, we study the nonequilibrium imaginary-time relaxation dynamics in the $J\text{\ensuremath{-}}{Q}_{2}$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss possible experimental realizations in devices of quantum computers.