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

TL;DR

This paper explores how the von Neumann entropy relates to optimal spin transport in an Heisenberg XXZ chain connected to magnetic reservoirs, revealing that maximum current aligns with entropy extrema and near-pure states.

Contribution

It provides explicit solutions for the stationary states of the XXZ chain under boundary driving and links entropy extrema to maximal spin currents, highlighting conditions for near-pure optimal transport.

Findings

Maximal spin current occurs near extrema of von Neumann entropy.

In strong coupling, minimal VNE approaches zero, indicating near-pure states for optimal transport.

Maximal transport states can coincide with entropy extrema depending on parameters.

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.