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Acta Physica Sinica

The effect of impurity on the entanglement between the normal lattice in three-qubit Heisenberg XX chain

Tao Zhang, Xiao-Qiang Xi, Rui‐Hong Yue, (1)西安邮电学院应用数理系，西安 710061; (2)西北大学现代物理研究所，西安 710069

Published Jan 1, 2004• 10 citations
Publisher

Abstract

In this paper,we study the effect of impurity on the thermal entanglement between the normal lattice in three-qubit Heisenberg XX chain,and give the analytical expression of the concurrence.According to the discussion of our result,we find that the impurity parameter has a great effect on the pairwise thermal entanglement,it even can change the characters of the entanglement to some degree.

DOI
10.7498/aps.53.2755

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In this paper,we study the effect of impurity on the thermal entanglement between the normal lattice in three-qubit Heisenberg XX chain,and give the analytical expression of the concurrence.According to the discussion of our result,we find that the impurity parameter has a great effect on the pairwise thermal entanglement,it even can change the characters of the entanglement to some degree.
In this paper,we investigated the influence of impurity on the entanglement between the normal lattice in a three-qubit Ising chain.The results show that the impurity parameter has great effects on the pairwise entanglement,it can make the normal lattice disentangled and sometimes at certain regions of magnetic field B and temperature T,it can even make the concurrence between the normal lattice greater than the general pairwise entanglement of three qubits(J1=J) or two qubits(J1=0).When T=0,for the case of antiferromagnet with the conditions of θ=π/2,B→0 or θ→0,B2J,the concurrence shows a square-wave structure with the variation of the impurity parameter J1.
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 pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interactions was investigated by using the concurrence measure. The results show that for the nearest-neighbor sites, the entanglement may be improved or suppressed depending on the magnitudes of the NNN coupling constant J, while for the next-nearest-neighbor sites, it always increases with the increase of |J|. The critical temperature Tc decreases with the increase of J for the nearest-neighbor entanglement and increases with the increase of |J| for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XX model still can be used to create the entangled W states of three and four qubits, and that the presence of NNN coupling has no effect on the creation of four-qubit W states, while it shifts the instant of time at which the three-qubit W states are created.
For a three-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modelling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.