We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of ``local'' macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model. We focus on the scaling regime, where the bandwidth of the fermions in the leads is larger than all the other energies, so that the lattice and the continuum versions of the model become equivalent. Using time-dependent density matrix renormalization group simulations initialized with states having different densities in the two leads we extend the results of Boulat, Saleur and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008)] concerning the current-voltage (I-V ) curves, for several values of the interaction strength U . We estimate numerically the Kondo scale TB and the exponent b(U ) associated to the tunneling of the fermions from the leads to the dot. Next we analyze the quantum entanglement properties of the steady states. We focus in particular on the entropy rate α, describing the linear growth with time of the bipartite entanglement in the system. We show that, as for the current, α/TB is described by some function of U and of the rescaled bias V /TB. Finally, the spatial structure of the entropy profiles is discussed. arXiv:1707.06111v2 [cond-mat.str-el] 5 Dec 2017 J. From now we take J = 1 = , thus defining the unit of time and energy. Left leadRight lead dot J J' J' J U