Stationary states in a free fermionic chain from the quench action method

We employ the quench action method 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 nonequilibrium steady state 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.

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