Thermalization of locally perturbed many-body quantum systems

TL;DR

This paper analytically demonstrates that systems satisfying the weak eigenstate thermalization hypothesis (ETH) exhibit thermalization under certain far-from-equilibrium initial conditions, advancing understanding of quantum thermalization mechanisms.

Contribution

The work provides a rigorous analytical proof that weak ETH systems thermalize for specific classes of initial states, expanding the theoretical framework of quantum thermalization.

Findings

Weak ETH implies thermalization for certain initial states

Thermalization occurs after quantum quenches in weak ETH systems

Analytical demonstration extends understanding of quantum thermalization

Abstract

Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical physics. The well-known eigenstate thermalization hypothesis (ETH) is presumed to be a key mechanism, but has defied rigorous verification for generic systems thus far. A weaker variant (weak ETH), by contrast, is provably true for a large variety of systems, including even many integrable models, but its implications with respect to the problem of thermalization are still largely unexplored. Here we analytically demonstrate that systems satisfying the weak ETH exhibit thermalization for two very natural classes of far-from-equilibrium initial conditions: the overwhelming majority of all pure states with a preset non-equilibrium expectation value of some given local observable, and the Gibbs states of a Hamiltonian which subsequently is subject to a quantum quench in the form of a sudden change of some local system properties.