Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well described by an effective non-Hermitian Hamiltonian generating a time evolution that allows eigenstates to decay and dissipate to the environment. In this framework, quantum coherent scaling is traditionally tied to the appearance of dark states, where the effect of dissipation becomes negligible. Here, we discuss the universal dynamical scaling after a sudden quench of the non-Hermitian $O(N)$ model Hamiltonian. While universality is generally spoiled by non-Hermiticity, we find that for a given set of internal parameters short-time scaling behavior is restored with an initial slip exponent profoundly different from that of closed quantum systems. This result is tied to the compensation of dissipation by interaction effects at short times leading to a prethermal dark state, where coherent many-body dynamics can be still observed.
Recent experimental and theoretical progress as well as the prospect of commercially viable quantum technologies have inspired great interest in the study of open quantum systems and their dynamics. Many open quantum systems are well described by an effective non-Hermitian Hamiltonian generating a time evolution that allows eigenstates to decay and dissipate to the environment. In this framework, quantum coherent scaling is traditionally tied to the appearance of dark states, where the effect of dissipation becomes negligible. Here, we discuss the universal dynamical scaling after a sudden quench of the non-Hermitian O(N) model Hamiltonian. While universality is generally spoiled by non-Hermiticity, we find that for a given set of internal parameters short-time scaling behavior is restored with an initial slip exponent profoundly different from that of closed quantum systems. This result is tied to the compensation of dissipation by interaction effects at short times leading to a prethermal dark state, where coherent many-body dynamics can be still observed.
A long-lived prethermal state may emerge upon a sudden quench of a quantum system. In this paper, we study a quantum quench of an initial {\it critical} state, and show that the resulting prethermal state exhibits a genuinely quantum and dynamical universal behavior. Specifically, we consider a scenario where the "speed of light" characterizing the propagation of local perturbations is suddenly quenched at criticality. We also find that the system approaches the prethermal state in a universal way described by a new exponent that characterizes a kind of quantum aging.
Open quantum systems can host dark or subradiant states whose decay is highly suppressed. While these states have been extensively studied in the few-excitation regime, their impact on the many-body dynamics remains largely unexplored. Here, we study a spin chain subject to correlated dissipation on neighboring sites, which admits a single-particle dark state at zero momentum. We show that the single-particle dark state qualitatively alters the many-body dynamics at long times, and identify its distinct universal behavior. While the zero-momentum mode is dark at the single-particle level, it decays slowly as 1/logt as it becomes dressed by other modes through a dissipation-induced nonlinearity. We demonstrate that the momentum distribution takes a universal scaling form in kt, and the total density decays as 1/tlogt. Our results further elucidate the origin of the conflicting results in recent works. Finally, we corroborate the analytics with matrix product state simulations and show that the same universal behavior persists for soft-core interactions, underscoring the universality of the emergent dynamics.
Dynamical quantum phase transitions (DQPTs) are non-equilibrium transitions characterized by the orthogonality between an initial quantum state and its time-evolved counterpart following a sudden quench. Recently, studies of this phenomenon have been extended beyond closed quantum systems to include environmental interactions, often modeled through non-Hermitian effects. However, because non-Hermitian descriptions neglect both quantum jump processes and interaction effects, the ultimate fate of interacting quantum systems under full open-system quantum dynamics remains an open question. In this paper, by incorporating both interactions and full Liouvillian dynamics, we prove that DQPTs in open quantum systems remain robust when subject to either particle loss or particle gain alone, but are generically smeared out when both processes coexist, as a result of many-body particle backflow. Furthermore, we uncover a non-perturbative dynamical effect: even a weak admixture of gain (loss) into a system with loss (gain) can dramatically reshape the long-time behavior of DQPT dynamics, leading to substantial deviations over time. These phenomena--including the universal smearing of DQPTs and the emergence of large dynamical deviations in the long-time limit--arise intrinsically from non-equilibrium many-body effects in open quantum systems. Our findings are general and substantiated by both analytical arguments and numerical simulations.
We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.
We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.
While imaginary-time evolution has long served as a standard paradigm for ground-state preparation in numerical simulations and quantum devices, its intrinsic dynamical properties has been largely overlooked. Here, we investigate the short-imaginary-time critical dynamics in quantum systems with boundaries. A universal scaling theory is developed and verified in the two-dimensional quantum Ising model, uncovering rich dynamic critical behaviors dictated by boundary universality classes. For ordered initial states, the boundary order parameter Ms decays with imaginary time τ as Ms∝τ−β1/νz, where β1 denotes the boundary order parameter exponent, and ν and z correspond to the correlation length exponent and the dynamic exponent, respectively. For disordered initial states, the autocorrelation of the boundary order parameter is governed by a novel critical exponent θ1, which is closely related to the critical initial slip behavior of Ms characterized by the corresponding exponent θ1′. In contrast to its positive bulk counterpart, the boundary initial-slip exponent θ1′ is negative for the ordinary transition while remaining positive for the special transition. Although the static universality classes of d-dimensional quantum phase transitions generally coincide with those of (d+1)-dimensional classical phase transitions, we show that θ1 does not follow this conventional quantum-classical mapping. We further discuss the implications of our results for more exotic forms of boundary criticality. Our findings provide new physical insights into boundary critical dynamics and offer a novel route for probing exotic boundary critical behaviors in quantum many-body systems.