Prethermalization at Low Temperature: The Scent of Long-Range Order

Nonequilibrium Dynamics and Weakly Broken Integrability

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model, we establish an analytical approach to real-time dynamics. The method addresses a broad range of timescales, from the intermediate regime of prethermalization to late-time thermalization. Predictions are given for the time evolution of physical quantities, including effective temperatures and thermalization rates. The approach provides conceptual links between perturbed quantum many-body dynamics and classical Kolmogorov-Arnold-Moser theory. In particular, we identify a family of perturbations which do not cause thermalization in the weakly perturbed regime.

Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalize at late times. We show that the full thermalizing dynamics can be described by the generalized hydrodynamics with diffusion and force terms, and we compare these predictions to numerical simulations. Finally, we provide an explanation for the slow thermalization rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterized by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalization can display prethermal plateau and relaxation dynamics with long polynomial finite-time corrections.

Typicality of Prethermalization

Prethermalization refers to the remarkable relaxation behavior which an integrable many-body system in the presence of a weak integrability-breaking perturbation may exhibit: After initial transients have died out, it stays for a long time close to some nonthermal steady state, but on even much larger time scales, it ultimately switches over to the proper thermal equilibrium behavior. By extending Deutsch's conceptual framework from Phys. Rev. A 43, 2046 (1991)PLRAAN1050-294710.1103/PhysRevA.43.2046, we analytically predict that prethermalization is a typical feature for a very general class of such weakly perturbed systems.

Detecting Equilibrium and Dynamical Quantum Phase Transitions in Ising Chains via Out-of-Time-Ordered Correlators

Out-of-time-ordered (OTO) correlators have developed into a central concept quantifying quantum information transport, information scrambling, and quantum chaos. In this Letter, we show that such an OTO correlator can also be used to dynamically detect equilibrium as well as nonequilibrium phase transitions in Ising chains. We study OTO correlators of an order parameter both in equilibrium and after a quantum quench for different variants of transverse-field Ising models in one dimension, including the integrable one as well as nonintegrable and long-range extensions. We find for all the studied models that the OTO correlator in ground states detects the quantum phase transition. After a quantum quench from a fully polarized state, we observe numerically for the short-range models that the asymptotic long-time value of the OTO correlator signals still the equilibrium critical points and ordered phases. For the long-range extension, the OTO correlator instead determines a dynamical quantum phase transition in the model. We discuss how our findings can be observed in current experiments of trapped ions or Rydberg atoms.