Thermalization timescales in a 1d Hubbard model with slightly broken integrability

Amy Cassidy, Vanja Dunjko, Maxim Olshanii +1 more

Laura Wadleigh, Nicholas Kowalski, Philip Russ +1 more

Federica Maria Surace, Olexei I. Motrunich

A quantum integrable system slightly perturbed away from integrability is typically expected to thermalize on timescales of order $\ensuremath{\tau}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}2}$, where $\ensuremath{\lambda}$ is the perturbation strength. We here study classes of perturbations that violate this scaling, and exhibit much longer thermalization times $\ensuremath{\tau}\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}2\ensuremath{\ell}}$ where $\ensuremath{\ell}>1$ is an integer. Systems with these ``weak integrability breaking'' perturbations have an extensive number of quasiconserved quantities that commute with the perturbed Hamiltonian up to corrections of order ${\ensuremath{\lambda}}^{\ensuremath{\ell}}$. We demonstrate a systematic construction to obtain families of such weak perturbations of a generic integrable model for arbitrary $\ensuremath{\ell}$. We then apply the construction to various models, including the Heisenberg, XXZ, and XYZ chains, the Hubbard model, models of spinless free fermions, and the quantum Ising chain. Our analytical framework explains the previously observed evidence of weak integrability breaking in the Heisenberg and XXZ chains under certain perturbations.

修一 村上

Joseph Durnin, M. J. Bhaseen, Benjamin Doyon

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.

Antonio Picano, Martin Eckstein

We study the melting of long-range antiferromagnetic order in the Hubbard model after an interaction quench, using nonequilibrium dynamical mean-field theory. From previous studies, the system is known to quickly relax into a prethermal symmetry-broken state. Using a convergent truncation of the memory integrals in the Kadanoff Baym equations, we unravel the subsequent relaxation dynamics of this state over several orders of magnitude in time. At long times, the prethermal state can be characterized by a single slow variable, which is related to the conduction band population. The dynamics of this variable is highly nonlinear, with a pronounced speedup once the gap falls below a certain value. This behavior indicates that nonthermal order can be self-sustained on some timescale because of a thermalization bottleneck is provided by the gap opened by the long-range order itself. These results cannot be reproduced using simple Fermi's golden rule estimate for the evolution of the conduction band population, and are distinct from the conventional scenario for the relaxation of prethermal states, in which a slow thermalization follows a rapid prethermalization.