Prethermal memory loss in interacting quantum systems coupled to thermal baths

Abstract

We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for sufficiently large field gradients and initial energies, the entropy peaks in time and almost reaches its largest possible value (corresponding to the maximally mixed state), long before the system relaxes to thermal equilibrium. This entropy peak signals an effective prethermal memory loss and, relative to the time where it occurs, the system is found to exhibit a simple scaling behavior in space and time. By comparing the system's dynamics to that of a simplified model, the underlying mechanism is found to be related to the localization property of the Wannier-Stark system, which favors dissipative coupling between eigenstates that are close in energy.

Environment-induced decay dynamics of anti-ferromagnetic order in Mott-Hubbard systems

“…As a result, we were able to find simple evolution equations for several observables, such as total particle number and total angular momentum, which are valid for arbitrary lattices. For zero-temperature reservoirs, these evolution equations already indicate the emergence of very different relaxation time scales, as also found in other examples 31,39,40,[51][52][53] , see Fig. 3.…”

“…As a result, we find two vastly different relaxation time scales -as already observed in many other systems and scenarios, see, e.g., Refs. 31,39,40,[51][52][53] . A more quantitative analysis of these two time scales will be presented in the next section.…”

Indication of critical scaling in time during the relaxation of an open quantum system

“…Since the maximum entropy corresponds to a unique state, the maximally mixed state , after approaching , the dynamics is expected to become (approximately) independent of the details of the initial state. This happens long before the spin system has thermalized 29 . Such a prethermal memory loss is observed in the experiment for both magnetic field regimes.…”