Energy as Entanglement Witness in Bilinear-Biquadratic Spin-1 Chain

Energy is introduced as an entanglement witness to describe the entanglement property of a quantum system. The thermal equilibrium system is guaranteed to be entangled when system is cooled down below the entanglement temperature TE. By virtue of this concept we exploit the minimum separable state energy and entanglement temperature TE of the bilinear-biquadratic antiferromagnetic spin-1 chain model. We numerically calculate TE for arbitrary values of the strength of biquadratic exchange interaction Q up to N = 7. We find TE decreases with Q for fixed N when Q is between -3 and 1/3 (J = 1). In this regime TE also decreases with N for fixed Q and varies slowly for large N. While the thermal system is always entangled when Q is smaller than -3.