Title: Entanglement and quantum transport in integrable systems,
Abstract: Understanding the entanglement structure of out-of-equilibrium many-body
systems is a challenging yet revealing task. Here we investigate the
entanglement dynamics after a quench from a piecewise homogeneous initial state
in integrable systems. This is the prototypical setup for studying quantum
transport, and it consists in the sudden junction of two macroscopically
different and homogeneous states. By exploiting the recently developed
integrable hydrodynamic approach and the quasiparticle picture for the
entanglement dynamics, we conjecture a formula for the entanglement production
rate after joining two semi-infinite reservoirs, as well as the steady-state
entanglement entropy of a finite subregion. We show that both quantities are
determined by the quasiparticles created in the Non Equilibrium steady State
(NESS) appearing at large times at the interface between the two reservoirs.
Specifically, the steady-state entropy coincides with the thermodynamic entropy
of the NESS, whereas the entropy production rate reflects its spreading into
the bulk of the two reservoirs. Our results are numerically corroborated using
time-dependent Density Matrix Renormalization Group (tDMRG) simulations in the
paradigmatic XXZ spin-1/2 chain.