Thermalization under randomized local Hamiltonians

TL;DR

This paper investigates how quantum systems thermalize after a quench under random local Hamiltonians, showing that most such Hamiltonians lead to rapid local thermalization to an infinite temperature state.

Contribution

It introduces a framework for analyzing thermalization under random local Hamiltonians and demonstrates that most unitarily equivalent local Hamiltonians cause quick local thermalization.

Findings

Almost all bases lead to local equilibration to the infinite temperature state.

Thermalization occurs in algebraically small time for most unitarily equivalent local Hamiltonians.

Small Fourier transform of spectral density correlates with thermalization.

Abstract

Recently, there have been significant new insights concerning conditions under which closed systems equilibrate locally. The question if subsystems thermalize---if the equilibrium state is independent of the initial state---is however much harder to answer in general. Here, we consider a setting in which thermalization can be addressed: A quantum quench under a Hamiltonian whose spectrum is fixed and basis is drawn from the Haar measure. If the Fourier transform of the spectral density is small, almost all bases lead to local equilibration to the thermal state with infinite temperature. This allows us to show that, under almost all Hamiltonians that are unitarily equivalent to a local Hamiltonian, it takes an algebraically small time for subsystems to thermalize.