Quantum quench from a thermal tensor state: Boundary effects and generalized Gibbs ensemble

Abstract

We consider a quantum quench in a noninteracting fermionic one-dimensional field theory. The system of size $L$ is initially prepared into two halves $\mathcal{L}$ $([\ensuremath{-}L/2,0])$ and $\mathcal{R}$ $([0,L/2])$, each of them thermalized at two different temperatures ${T}_{\mathcal{L}}$ and ${T}_{\mathcal{R}}$, respectively. At a given time, the two halves are joined together by a local coupling and the whole system is left to evolve unitarily. For an infinitely extended system $(L\ensuremath{\rightarrow}\ensuremath{\infty})$, we show that the time evolution of the particle and energy densities is well described via a hydrodynamic approach which allows us to evaluate the correspondent stationary currents. We show, in such a case, that the two-point correlation functions are deduced, at large times, from a simple nonequilibrium steady state. Otherwise, whenever the boundary conditions are retained (in a properly defined thermodynamic limit), any current is suppressed at large times, and the stationary state is described by a generalized Gibbs ensemble, which is diagonal and depends only on the post-quench mode occupation.