Entanglement in a molecular three-qubit system

TL;DR

This paper investigates the entanglement properties of a molecular three-qubit system modeled by the Heisenberg spin Hamiltonian, analyzing how quantum phase transitions and temperature affect pairwise entanglement.

Contribution

It provides a detailed analysis of ground and thermal state entanglement in a three-qubit molecular system, including the effects of anisotropy and external magnetic fields.

Findings

Identification of entanglement thresholds and gap temperatures.

Quantification of nearest-neighbour and next-nearest-neighbour entanglement.

Relevance to molecular $Cr_{7}Ni$-$Cu^{2+}$-$Cr_{7}Ni$ systems.

Abstract

We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first order quantum phase transitions by tuning two parameters, $x$ and $y$, of the Hamiltonian to specific values. The three-qubit chain is open ended so that there are two types of pairwise entanglement : nearest-neighbour (n.n.) and next-nearest-neighbour (n.n.n.). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters $x$, $y$ and the temperature $T$. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter $x$. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular $Cr_{7}Ni$-$Cu^{2+}$-$Cr_{7}Ni$ complex which serves as a three-qubit system at sufficiently low temperatures.