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

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).

6 pages, 1 figure

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• Entanglement negativity and entropy in non-equilibrium conformal field theory
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit