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 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.
The nonequilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e., a sudden change of a parameter in the Hamiltonian, such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e., dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of an N-component ${\ensuremath{\varphi}}^{4}$ model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-N limit, which is complementary to our earlier renormalization-group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry-broken phase and at the upper critical dimension. By connecting the long-time limit of fluctuations and response, we introduce a distribution function that shows that the system remains nonthermal and exhibits quantum coherence even on long time scales.
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.
We reveal a prethermal dynamical regime upon suddenly quenching to the vicinity of a quantum phase transition in the time evolution of one-dimensional spin chains. The prethermal regime is analytically found to be self-similar and its duration is governed by the ground-state energy gap. Based on analytical insights and numerical evidence, we show that this dynamical regime universally exists independently of the location of the probe site, the presence of weak interactions, or the initial state. The resulting prethermal dynamics leads to an out-of-equilibrium scaling function of the order parameter in the vicinity of the transition. Our theory suggests that sudden quench dynamics, besides probing quantum phase transitions, may give rise to a universal critical slowing down near the critical point.
We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case in which the initial state is a critical ground state, or the postquenched Hamiltonian is at a critical point of equilibrium quantum phase transition, or both of them are critical. In such a ``critical quench,'' we find very interesting real-time dynamical scaling behaviors and we find crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors ${t}^{\ensuremath{-}3/2}$ and ${t}^{\ensuremath{-}3/4}$ in the noncritical quenches may be changed to ${t}^{\ensuremath{-}1}$ and ${t}^{\ensuremath{-}1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and we find another crossover exponent. All the results are related to the gap-closing properties of the energy spectrum of the critical points.
We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasiparticle excitation that ensure that Kibble-Zurek scaling persists. The emergence of effective thermal equilibrium behavior following a sudden quench toward criticality is also investigated, with focus on the long-time expectation value of the quasiparticle number operator. Despite the integrability of the XY model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches toward a multicritical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.
Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate here the dynamics of an isolated quantum system represented by a scalar ${\ensuremath{\phi}}^{4}$ theory after a global quench of the potential close to a dynamical critical point. We demonstrate that, within a prethermal regime, the time dependence of the relevant correlations is characterized by a short-time universal exponent, which we calculate at the lowest order in a dimensional expansion.