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.

Figure 1

The integration contour $C_t$ in the complex plane of $z=e^{i{\varphi }^{\prime }}$: it consists of the blue and red closed curves depicted in the figure. The region where $\text{Im}\left[\varepsilon \right(z\left)\right]>0$ is colored in gray, whereas the blue region corresponds to $\text{Im}\left[\varepsilon \right(z\left)\right]<0$. The contour $C_t$ avoids the essential singularity at the origin of the integrand in (17).