Optimal transport and von Neumann entropy in an Heisenberg XXZ chain out of equilibrium

Abstract

In this paper we investigate the spin currents and the von Neumann entropy (VNE) of an 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 extrema of the VNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. 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.

8 pages, 7 figures

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• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Anomalous currents in driven XXZ chain with boundary twisting at weak coupling or weak driving
• Full decoherence induced by local fields in open spin chains with strong boundary couplings
• Dissipative cooling towards phantom Bethe states in boundary driven XXZ spin chain
• Switching pure states of the dissipative Heisenberg XXZ chain by local magnetic fields