Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis   in a One-Dimensional Interacting Bose gas
  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. 
Tatsuhiko N. Ikeda, Yu Watanabe, and Masahito Ueda
cond-mat.stat-mech cond-mat.quant-gas quant-ph