Boundary and impurity effects on entanglement of Heisenberg chains

TL;DR

This paper investigates how boundary conditions and impurities affect entanglement in open Heisenberg chains, revealing oscillatory behaviors and impurity-induced entanglement thresholds.

Contribution

It provides new insights into boundary and impurity effects on entanglement in Heisenberg models, including oscillation patterns and entanglement thresholds.

Findings

Entanglement oscillates with a two-site period under open boundaries.

Mean pairwise entanglement correlates with ground-state energy per site.

Impurities induce entanglement thresholds depending on coupling strength.

Abstract

We study entanglement of a pair of qubits and the bipartite entanglement between the pair and the rest within open-ended Heisenberg $XXX$ and XY models. The open boundary condition leads to strong oscillations of entanglements with a two-site period, and the two kinds of entanglements are 180 degree out of phase with each other. The mean pairwise entanglement and ground-state energy per site in the $XXX$ model are found to be proportional to each other. We study the effects of a single bulk impurity on entanglement, and find that there exists threshold values of the relative coupling strength between the impurity and its nearest neighbours, after which the impurity becomes pairwise entangled with its nearest neighbours.