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

Abstract

We rigorously analyse global tripartite entanglement in a mixed-spin ($1$,$1/2$,$1$) Heisenberg trimer under varying exchange couplings, magnetic fields, and temperatures. Entanglement is quantified using the geometric mean of all three bipartite negativities, enabling us to map precisely the regions of spontaneous global entanglement and to classify the tripartite states according to the distribution of reduced bipartite correlations. We further investigate the thermal stability of entanglement across the full parameter space, with particular focus on the experimentally realised trimer [Ni(bapa)(H${}_2$O)]${}_2$Cu(pba)(ClO${}_4$)${}_2$ (bapa = bis(3-aminopropyl)amine; pba = 1, 3-propylenebis(oxamato)), where global entanglement is predicted to persist up to $\sim 100$ K and magnetic fields approaching 210 T. Notably, we observe a thermally induced activation of robust entanglement in regions with a biseparable ground state, reaching values close to $1/2$ - a phenomenon not previously reported. Finally, we propose a connection between the theoretically predicted tripartite entanglement and experimentally measurable quantities.