Stationary states in a free fermionic chain from the Quench Action Method

TL;DR

This paper uses the Quench Action Method to analyze the long-time behavior of two joined free fermionic chains initially at different temperatures, revealing regimes of non-equilibrium steady states and thermalization.

Contribution

It applies the Quench Action Method to a geometrical quantum quench, identifying different stationary regimes and the conditions for non-equilibrium steady states and thermalization.

Findings

Existence of a non-equilibrium steady state with energy current

Identification of a longer time-scale for thermalization in GGE

Dependence of stationary regimes on observation time and system size

Abstract

We employ the Quench Action Method (QAM) for a recently considered geometrical quantum quench: two free fermionic chains initially at different temperatures are joined together in the middle and let evolve unitarily with a translation invariant Hamiltonian. We show that two different stationary regimes are reached at long times, depending on the interplay between the observation time scale T and the total length L of the system. We show the emergence of a non-equilibrium steady state (NESS) supporting an energy current for observation time T much smaller than the system size L. We then identify a longer time-scale for which thermalization occurs in a Generalized Gibbs Ensemble (GGE).