title: Optimal transport and von Neumann entropy in a Heisenberg XXZ chain out of equilibrium.
abstract: In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states.
authors.affiliation: Dipartimento di Fisica E.R. Caianiello, Università di Salerno, Via Ponte don Melillo, 84084 Fisciano, Salerno, Italy.
authors.forename: Mario
authors.initials: M
authors.lastname: Salerno
authors.forename: Vladislav
authors.initials: V
authors.lastname: Popkov
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D019277:Entropy; D015233:Models, Statistical