Robust global tripartite entanglement in a mixed spin-($1$,$1/2$,$1$) Heisenberg trimer

TL;DR

This paper investigates the robustness and distribution of tripartite entanglement in a mixed-spin Heisenberg trimer, analyzing how it persists under various conditions and its potential experimental realization.

Contribution

It introduces a detailed analysis of global tripartite entanglement in a mixed-spin trimer, including its thermal stability and experimental relevance, using negativity as a quantifier.

Findings

Global entanglement persists up to 100 K and 210 T.

Thermally activated entanglement occurs in biseparable ground states.

High entanglement magnitude nearly reaches 1/2.

Abstract

We rigorously analyze the global tripartite entanglement in a Heisenberg trimer with mixed spins-($1$,$1/2$,$1$) under varying exchange couplings between dissimilar and identical spins, magnetic fields, and temperatures. The global tripartite entanglement is quantified using the geometric mean of all three bipartite contributions, evaluated through negativity. We precisely map the regions of parameter space in which the trimer system exhibits spontaneous global entanglement. In addition, we classify the nature of the tripartite entangled states based on the distribution of reduced bipartite negativities among the spin dimers in the trimer. We further examine the thermal stability of global tripartite entanglement throughout the full parameter space. Special attention is given to the theoretical prediction of thermal robustness in a real three-spin complex, [Ni(bapa)(H$_2$0)]$_2$Cu(pba)(ClO$_4$)$_2$, where bapa stands for bis($3$-aminopropyl)amine, and pba denotes $1$,$3$-propylenebis(oxamato), which serves as an experimental realization of the mixed-spin ($1$,$1/2$,$1$) Heisenberg trimer. Notably, global entanglement in this system is predicted to persist up to approximately $100$ K and magnetic fields approaching $210$ T. Moreover, we uncover a thermally induced activation of robust global entanglement in regions where the ground state is biseparable. The magnitude of this thermal entanglement is remarkably high, nearly reaching a value of $1/2$, which has not been reported before. Finally, we propose a connection between the theoretically predicted tripartite entanglement, quantified via negativity derived from the density matrix, and the quantities measured directly or indirectly from various experiments.