Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

TL;DR

This paper investigates how closed finite quantum lattice systems reach and maintain thermal equilibrium, demonstrating conditions for equilibration, local thermalization, and stability against disturbances with finite-size bounds.

Contribution

It provides rigorous proofs for thermalization, local thermalization, and stability in finite quantum lattice systems with finite-size bounds, advancing understanding in quantum thermodynamics.

Findings

States with exponentially decaying correlations equilibrate after a quantum quench

Equilibrium states are locally thermal under certain conditions

Thermal states with exponential decay of correlations are stable against local disturbances

Abstract

Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications.