Entanglement in heterogeneous spin-$(1,\frac{1}{2})$ and homogeneous spin-1 systems

Abstract

We study the bipartite entanglement of two general classes of heterogeneous spin-($1,\frac{1}{2}$) and homogeneous spin-1 systems. By employing the spin correlation functions, we obtain the reduced two-spin density matrix (DM) and the negativity for these two classes of quantum spin models. We show explicitly that in addition to the one and two-point correlations, the triad and quad correlations ($t_{αβ}^δ=\la S_αS_βs_δ\ra$ and $q_{αβ}^{δγ}=\la S_αS_βs_δs_γ\ra$ where $\alpha ,\beta ,\delta ,\gamma =\pm ,z$) play crucial role in the bipartite entanglement between spins $s>1/2$. These correlations represent the spin $\frac{1}{2}$-quadrupole and quadrupole-quadrupole correlations, respectively. These correlations do not appear in the spin-$\frac{1}{2}$ models. Our results are general and applicable to the different several models of interest with higher reflectional, translational, spin-flip and U(1) symmetries. The entanglement of many attractive models are investigated.

arXiv comment9 pages, 1 figure, submitted