Exact steady state of the open XX-spin chain: entanglement and transport properties

TL;DR

This paper derives the exact steady state of an open XX-spin chain with boundary heat baths, analyzing entanglement and transport properties, and providing explicit formulas and algorithms for bipartite entanglement.

Contribution

It provides the first analytic expression for the stationary state of an open XX-spin chain with boundary baths and develops an algorithm to study entanglement distribution.

Findings

Explicit stationary state expression for the open XX-spin chain.

Identification of sink and source terms in spin flow.

Algorithm for computing bipartite entanglement along the chain.

Abstract

We study the reduced dynamics of open quantum spin chains of arbitrary length $N$ with nearest neighbour $XX$ interactions, immersed within an external constant magnetic field along the $z$ direction, whose end spins are weakly coupled to heat baths at different temperatures, via energy preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behaviour with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures.