Eigenstate thermalization within isolated spin-chain systems

TL;DR

This paper investigates how isolated spin-chain systems thermalize, showing that non-integrable models follow ETH while integrable ones deviate, with finite-size effects and transport properties analyzed.

Contribution

It demonstrates the validity of ETH in non-integrable spin chains and characterizes deviations in integrable systems, including finite-size scaling and transport behavior.

Findings

Non-integrable models obey ETH for diagonal matrix elements.

Integrable models show deviations from ETH, resembling noninteracting fermions.

Finite-size scaling relates crossover to scattering length.

Abstract

The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for non-integrable models comply with the eigenstate thermalization hypothesis (ETH), the integrable systems show evident deviations and similarity to properties of noninteracting many-fermion models. The finite-size scaling reveals that the crossover between two regimes is given by a scale closely related to the scattering length. Low-frequency off-diagonal matrix elements related to d.c. transport quantities in a generic system also follow the behavior analogous to the ETH, however unrelated to the one of diagonal elements.