Time-dependent generalized Gibbs ensembles in open quantum systems

TL;DR

This paper extends the use of generalized Gibbs ensembles to describe the long-time behavior of weakly perturbed, integrable quantum systems far from equilibrium, using numerical simulations of the Heisenberg model.

Contribution

It introduces a time-dependent generalized Gibbs ensemble framework for non-equilibrium steady states in perturbed integrable systems, validated through numerical comparisons.

Findings

GGE accurately describes steady states under weak perturbations.

Time-dependent Lagrange parameters follow simple rate equations.

Numerical results match theoretical predictions for the Heisenberg model.

Abstract

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which both break integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time-evolution on long time-scales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.