Dynamical Crossovers in Prethermal Critical States

Abstract

We study the prethermal dynamics of an interacting quantum field theory with a 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 non-equilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a non-perturbative large-N limit.Introduction -An isolated many-body system, suddenly brought out of equilibrium, can linger over a nonthermal quasi-steady state before thermalization occurs at later times triggered by inelastic scattering processes. This phenomenon, known as prethermalization, is ubiquitous in physics: first predicted in the context of heavy-ion collisions [1] and early-universe inflationary dynamics [2], it has been only recently recognized in condensed matter and cold-atoms physics [3].Prethermal states can host a novel class of critical phenomena, since the gap associated with these nonequilibrium (NEQ) states can vanish upon choosing properly the initial conditions and parameters of the system. Quenching a quantum many-particle system above or below the corresponding critical points results in qualitatively different NEQ dynamics [4,5]. For instance, in the case of an interacting bosonic quantum field, quenching above or below its dynamical critical point induces respectively an exponential relaxation of local observables or a coarsening dynamics of correlation functions [6][7][8]. By quenching, instead, close to the dynamical critical point, correlation functions display non-equilibrium dynamical scaling [5,[8][9][10] similar to critical aging in classical dissipative systems [11,12] with a consequent delay of thermalization and stabilization of the associated prethermal states. These NEQ dynamical critical points can both be of quantum and classical nature, depending on the strength of the quantum quench performed at initial times [9,10].Interestingly, a recent experiment [13] has observed the emergence of dynamical scaling in a one-dimensional twocomponent Bose gas quenched close to criticality. The correlation length of the order parameter displayed there a dynamical crossover between a short-time critical and a long-time non-critical regime. This suggests the possibility to explore the variety of the dynamical critical points occurring in the prethermal dynamics of a quantum many-body system via quantum quenches, which expose the temporal crossover between different scaling behaviours.In this work, we propose a minimal model in which it

Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality

“…Because Ω 0c is the pre-quench a relevant scale [54,55], we take 1/Ω 0c → 0 and define Ω 0 ≡ Ω 0q . As we mentioned, Under such simplification, K ± = ± ω 0k 2ω k .…”

“…2 (b) shows the temporal crossover of the initial slip exponent θ, where θ < 0 for large enough N in the regime governed by the ECIFP and θ > 0 in the regime governed by the DCIFP.Discussion.-The observability of these nonequilibrium universal scaling behaviors relies on a long thermalization time scale. In the present case, the thermalization can be understood as the generation of the dissipative term, γφ qφc , in the RG flow [52][53][54][55]65]. Accordingly, the RG equation ofγ ≡ γΛ −1 effectively sets the thermalization time scale.…”

“…As with its classical counterpart, a critical initial slip exponent can be defined to characterize the dynamical fingerprint of the initial state. However, unlike the classical case in which the short-time dynamics is completely controlled by a corresponding equilibrium critical point, short-time quantum critical dynamics in an isolated system can also be controlled by a dynamical fixed point, which is similar to a thermal fixed point for a purely bosonic field [52][53][54][55].In the context of equilibrium criticality, gapless Dirac fermions, which appear in various systems including graphene, the surface of topological insulators, and Weyl semimetals, lead to exotic quantum phase transitions [56]. The best known example is the chiral Ising universality class [57][58][59][60], in which the gapless Dirac fermion is coupled to a bosonic field via a Yukawa coupling.…”

“…For a quench of the type described above, the initial state information is contained in the free boson Keldysh propagator which reads [62]where ω 2 0k = k 2 + Ω 2 0 and ω 2cos ω k (t−t ), which shows that Ω 0 plays a role of effective temperature, T eff = Ω0 4 . Because Ω 0 sets an effective temperature scale, one may expect a "quantum" to "classical" crossover similar to the bosonic system [55]. Moreover, given their inherently quantum nature, fermions are not expected to play a role in a classical phase transition [63,64].…”

“…As with its classical counterpart, a critical initial slip exponent can be defined to characterize the dynamical fingerprint of the initial state. However, unlike the classical case in which the short-time dynamics is completely controlled by a corresponding equilibrium critical point, short-time quantum critical dynamics in an isolated system can also be controlled by a dynamical fixed point, which is similar to a thermal fixed point for a purely bosonic field [52][53][54][55].…”