Prethermalization and Thermalization in Isolated Quantum Systems

TL;DR

This paper introduces a general framework for understanding prethermalization in quantum systems, showing how weak perturbations lead to intermediate equilibrium states and eventual thermalization, supported by numerical evidence.

Contribution

It proposes a simplified, more general setup for prethermalization involving weak perturbations breaking conservation laws, and derives the dynamics of the system's approach to equilibrium.

Findings

Intermediate equilibrium states govern system evolution

Time to global equilibrium scales as 1/g^2

Numerical calculations confirm theoretical predictions

Abstract

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a---possibly nonintegrable---reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order 1/g^2, where g is the perturbation strength. We also describe the leading correction to the time-dependent reference equilibrium state, which is, in general, of order g. The theory is well confirmed in numerical calculations of model Hamiltonians, for which we use a numerical linked cluster expansion and full exact diagonalization.