Short-time universal scaling in an isolated quantum system after a quench

Abstract

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 φ 4 theory after a global quench of the potential close to a dynamical critical point. We demonstrate that, within a pre-thermal 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.

Keldysh field theory for driven open quantum systems

“…As discussed in the previous sections, nonthermal steady states of driven-dissipative systems can show a large variety of universal features, such as scale invariance and effective long-wavelength thermalization. However, in a plethora of setups, aspects of universality can even be found in the time evolution, which approaches a steady state only in the limit τ → ∞ [45][46][47][311][312][313][314][315]. An example which identifies generic, universal features in the far from equilibrium dynamics in a strongly interacting one-dimensional system is discussed in the present section.…”

Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system

“…To this end, we employ the 2-particle irreducible (2PI) effective action approach on the closed Keldysh contour including corrections up to next-to-leading order (NLO) in 1/ N which allow the system to thermalize. The O(N )-model is a well established model for interacting many-body systems, both in condensed matter and cosmology3436373839404142434445. In particular, the presence of nontrivial interactions at NLO as well as the bosonic nature of excitations render the O(N )-model useful for studying heating of a driven many-body system to infinite temperature.…”

Entanglement properties of the critical quench ofO(N)bosons

“…For finite N , inelastic scattering will cause the system to thermalize after a time t * ∼ O (N ) resulting in diffusive rather than ballistic propagation of quasi-particles. For times t < t * the system is in a prethermal regime which is qualitatively similar 23,25 to the N → ∞ limit.…”

“…Rather, this exponent should actually be thought of as a boundary critical exponent 25,29 that governs the renormalization of the φ field at the temporal boundary t = 0. As it requires a temporal boundary it cannot be probed by local perturba-tions of the equilibrium critical state.…”

“…The above expressions can be obtained not only from solving the N = ∞ problem 24 , but also from performing a dimensional expansion 25 . The singularity as r → 2t and the suppression of the correlation function when r > 2t is given the following interpretation 1 .…”