Quantum Entanglement Generation in the Heterometallic Ni$^\text{2+}_4$Gd$_4^\text{3+}$ Complexes

Hamid Arian Zad; Michal Jaščur; Azam Zoshki; Ralph Kenna; Nerses Ananikian

doi:10.1103/w4yk-kclj

paper

Quantum Entanglement Generation in the Heterometallic Ni $_{4}^{2+}$ Gd $_{4}^{3+}$ Complexes

arXiv:2503.20311 · doi:10.1103/w4yk-kclj

Abstract

We investigate various types of quantum entanglement in the octanuclear heterometallic $3 d /4 f$ complexes denoted as Ni $_{4}^{2 +}$ Gd $_{4}^{3 +}$ under an external magnetic field, using the exact diagonalization approach. These molecular magnets, which can be effectively described by Heisenberg spin models, consist of two identical ${Ni_{2}^{2 +} Gd_{2}^{3 +}}$ cubane subunits bridged by acetate and hydroxide ligands. Our analysis reveals that their magnetization exhibits intermediate plateaus at low temperatures, indicating distinct ground states characteristic of Ni-containing compounds. Using negativity as a measure of quantum entanglement, we examine the influence of single-ion anisotropy and magnetic field on tetrapartite, bipartite, 1 $-$ 3 tangle, and 2 $-$ 2 tangle entanglements in two families of Ni $_{4}^{2 +}$ Gd $_{4}^{3 +}$ complexes: $(1)$ without anisotropy and $(2)$ with anisotropy. Complex $(1)$ exhibits strong bipartite entanglement between Ni ions, which persists up to $T \approx 3.0 K$ and $B \approx 4.0 T$ , but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between Gd $\dots$ Gd and Ni $\dots$ Gd pairs. In contrast, complex $(2)$ displays nonzero and sizable values for all types of entanglement considered. These findings emphasis the crucial role of single-ion anisotropy in generating and shaping the entanglement landscape of heterometallic Ni $_{4}^{2 +}$ Gd $_{4}^{3 +}$ complexes. Notably, we find that the 1 $-$ 3 tangle entanglement between a Ni ion and the remaining sites in a cubane unit serves as a reliable indicator of ground-state phase transitions, exhibiting distinct changes across phase boundaries irrespective of the presence of single-ion anisotropy.

arXiv comment13 pages, 7 figures

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Abstract

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Quantum Entanglement Generation in the Heterometallic Ni $_{4}^{2+}$ Gd $_{4}^{3+}$ Complexes