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Acta Physica Sinica

The effect of impurity on the thermal entanglement in three-qutrit spin-1 Heisenberg XXX chain

Qin Meng, Tian Dong-Ping, Tao Ying-Juan, (1)解放军理工大学理学院，南京 211101；西安交通大学理学院，西安 710049; (2)西安交通大学理学院，西安 710049; (3)西安邮电学院，西安 710061

Published Jan 1, 2008• 9 citations

Abstract

We investigate the impurity entanglement of 3-qutrit XXX-type Heisenberg chains in the presence of a uniform magnetic field along z axis by means of negativity. The entanglement is calculated as a function of the coupling constants J, impurity parameter J1, magnetic fields B and temperature T. Through calculating the negativity between sites 1 and (2,3) N1-23 and sites 3 and (1,2) N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of J1. The existence of magnetic fields B can obviously reduce the entanglement, and it is found that the limiting temperature Tc depends on the impurity parameter J1 but not on the magnetic field.

DOI: 10.7498/aps.57.5395

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We investigate the impurity entanglement of 3-qutrit XXX-type Heisenberg chains in the presence of a uniform magnetic field along z axis by means of negativity. The entanglement is calculated as a function of the coupling constants J, impurity parameter J1, magnetic fields B and temperature T. Through calculating the negativity between sites 1 and (2,3) N1-23 and sites 3 and (1,2) N12-3, we show that the critical temperature Tc above which the entanglement vanishes increases with the increase of J1. The existence of magnetic fields B can obviously reduce the entanglement, and it is found that the limiting temperature Tc depends on the impurity parameter J1 but not on the magnetic field.

We studied the entanglements of the Heisenberg XX chain with impurity in the presence of a uniform magnetic field along the z axes by means of negativity. Through analyzing NL-A and N1-A, we show that the critical temperatures for nonzero negativities depend on the impurity parameter J1 and the magnetic field B. It is also shown that as qubit L increases, the entanglements increase when L is odd but decrease when L is even. And the entanglements of the even-qubit chains are larger than those of the odd-qubit chains. The condition is similar with L=3 for NL-A when qubit L is odd, but the entanglements increase with the increase of even qubit L.

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.

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C.It is found that for impurity entanglement,C appears only when J1 J for J 0,and J1 0 for J 0,and in these two regions C increases with the increase of J1,so is the critical temperature Tc.When J1 |J|,C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1.For entanglement between the normal lattices,C appears only when J 0 and 2J J1 J,and initially increases with the increase of J1 and arrives at the maximum value Cmax =(e4JIT-3)/(e4JIT+3)before it decays to zero gradually,so is the critical temperature Tc with,however,the maximum value Tcmax = 4J/ln3.

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

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 .

In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit.We use negativity as a measure of entanglement in our study.We apply magnetic field, uniform and nonuniform field, on it.The results show that the entanglement decreases with increase in temperature.Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases.We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles.Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.