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arXiv:quant-ph/0501032 · Journal of Physics A Mathematical and General

Entanglement in spin-1 Heisenberg chains

Xiaoguang Wang, Haibin Li, Zhe Sun, You‐Quan Li

Published Sep 21, 2005• 39 citations
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Abstract

By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.

DOI
10.1088/0305-4470/38/40/014

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By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.
We investigate thermal and non-thermal quantum correlations in the one-dimensional spin-1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory-such as generalized concurrence, negativity, and various measures of quantum, classical, and total correlations in bipartite states-we demonstrate that these measures effectively identify quantum phase transitions (QPTs) at critical points. Our negativity analysis reveals nearly identical results at zero or very low temperatures. Importantly, we find that partial concurrence, defined with the reduced density matrix [Formula: see text], detects more quantum critical points than total concurrence. Additionally, we argue that spin chains with an odd number of spins are more effective than those with an even number in identifying QPTs.
The entanglement characteristics of the three-qutrit spin-one Heisenberg chain in the presence of one impurity site is investigated by using the concept of negativity. The results show that the existence of impurity can lead to an enhancement of both bipartite and pairwise entanglement for certain ranges of the impurity parameter, and the amount of entanglement can be controlled and tuned by varying the impurity parameter J1. The results also show that the thermal fluctuations always suppress the entanglement and as a result there exists a threshold temperature Tth after which the entanglement vanishes. Tth increases as J1 increases except the case for that of the pairwise negativity [Formula: see text] which measures entanglement between the two norm spins in the 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 T E . By virtue of this concept we exploit the minimum separable state energy and entanglement temperature T E of the bilinear-biquadratic antiferromagnetic spin-1 chain model. We numerically calculate T E for arbitrary values of the strength of biquadratic exchange interaction Q up to N = 7. We find T E decreases with Q for fixed N when Q is between -3 and 1/3 ( J = 1). In this regime T E 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.
The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field ( B ), a parameter b which controls the inhomogeneity of B , and the bilinear interaction parameters J x = J y ≠ J z on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of J z and lower values of B and b .