Effect of an uniaxial single-ion anisotropy on the quantum and thermal entanglement of a mixed spin-(1/2,$S$) Heisenberg dimer

TL;DR

This paper analytically investigates how uniaxial single-ion anisotropy influences quantum and thermal entanglement in a mixed spin-(1/2,S) Heisenberg dimer, revealing spin-dependent behaviors and conditions for maximal entanglement.

Contribution

It provides exact analytical results on the effects of anisotropy and spin magnitude on entanglement in mixed spin dimers, highlighting differences between integer and half-odd-integer spins.

Findings

Maximum entanglement occurs for antiferromagnetic ground states with half-odd-integer spins.

Integer spins with easy-plane anisotropy show increasing entanglement with spin size.

Higher spin magnitudes raise the threshold temperature for thermal entanglement.

Abstract

Exact analytical diagonalization is used to study the bipartite entanglement of the antiferromagnetic mixed spin-(1/2,$S$) Heisenberg dimer (MSHD) with the help of negativity. Under the assumption of uniaxial single-ion anisotropy affecting higher spin-$S$ ($S\!>\!1/2$) entities only, the ground-state degeneracy $2S$ is partially lifted and the ground state is two-fold degenerate with the total magnetization per dimer $\pm(S\!-\!1/2)$. It is shown that the largest quantum entanglement is reached for the antiferromagnetic ground state of MSHD with arbitrary half-odd-integer spins $S$, regardless of the exchange and single-ion anisotropies. Contrary to this, the degree of a quantum entanglement in MSHD with an integer spin $S$ for the easy-plane single-ion anisotropy, exhibits an increasing tendency with an obvious spin-$S$ driven crossing point. It is shown that the increasing spin magnitude is a crucial driving mechanism for an enhancement of a threshold temperature above which the thermal entanglement vanishes. The easy-plane single-ion anisotropy together with an enlargement of the spin-$S$ magnitude is other significant driving mechanism for an enhancement of the thermal entanglement in MSHD.