Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas

TL;DR

This paper investigates the eigenstate thermalization hypothesis (ETH) in a one-dimensional interacting Bose gas, revealing that weak ETH holds in the thermodynamic limit and comparing its role to typicality in thermalization.

Contribution

It provides a finite-size scaling analysis of ETH in the Lieb-Liniger model, highlighting the distinction between weak and strong ETH in integrable systems.

Findings

Weak ETH holds in the thermodynamic limit for the integrable system.

Weak ETH contributes only logarithmic corrections to thermalization.

Comparison shows typicality as a more dominant thermalization mechanism.

Abstract

By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.