Thermalization in a simple spin-chain model

TL;DR

This paper investigates how a one-dimensional spin-1/2 XX-model thermalizes after a local perturbation, providing detailed quantitative insights into the relaxation process in a simple quantum many-body system.

Contribution

It demonstrates that the spin-1/2 XX-model re-thermalizes after a local quench without assumptions beyond quantum mechanics, with detailed analysis of the relaxation dynamics.

Findings

System re-thermalizes for large times after local perturbation

Quantitative description of the relaxation behavior

Rich features observed in the relaxation dynamics

Abstract

We consider the common spin-1/2 XX-model in one dimension with open boundary conditions and a large but finite number of spins. The system is in thermal equilibrium at times t<0, and is subject to a weak local perturbation (quantum quench) at t=0. Focusing mainly on single-spin perturbations and observables, we show that the system re-thermalizes for sufficiently large times t>0 without invoking any unproven assumptions besides the basic laws of quantum mechanics. Moreover, the time-dependent relaxation behavior is obtained in quantitative detail and is found to exhibit a wealth of interesting features.