Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble

TL;DR

This paper introduces a systematic method to construct the generalized Gibbs Ensemble (GGE) as the optimal approximation to the true quantum state in non-equilibrium dynamics of integrable systems, improving the description of correlations.

Contribution

It presents a constrained minimization approach to systematically build the GGE and demonstrates its effectiveness in capturing higher-order correlations in a quenched Bose gas.

Findings

The correlated GGE better describes higher-order correlations.

Entropy of the GGE measures approximation quality.

Method applied successfully to a quenched Bose gas.

Abstract

We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to the time dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core bose gas. In contrast to the standard GGE, our correlated GGE properly describes the higher order correlation functions.