Low-temperature transport in out-of-equilibrium XXZ chains

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio \u3b6=x/t. By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures but described by non-trivial functions of \u3b6. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width \u394\u3b6 1dT emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of \u3b6 for all local observables

Entanglement evolution and generalised hydrodynamics: noninteracting systems

The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled

Quantum quench in the infinitely repulsive Hubbard model: The stationary state

We use the quench action approach to study the non-equilibrium dynamics after a quantum quench in the Hubbard model in the limit of infinite interaction. We identify a variety of low-entangled initial states for which we can directly compute the overlaps with the Hamiltonian's eigenstates. For these initial states, we analytically find the rapidity distributions of the stationary state characterising the expectation values of all local observables. Some of the initial states considered are not reflection symmetric and lead to non-symmetric rapidity distributions. To study such cases, we have to introduce a generalised form for the reduced entropy which measures the entropy restricted to states with non-zero overlap. The initial states considered are of direct experimental realisability and also represent ideal candidates for studying non-equilibrium dynamics in the Hubbard model for finite interactions