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Journal of Xi'an University of Post and Telecommunications

Entanglement of the Ising chain with impurity

Ming‐Liang Hu

Published Jan 1, 2008• 0 citations
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Abstract

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.

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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.
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.
By using the concept of concurrence, we study pairwise entanglement between the two end spins in the open-ended Heisenberg XXX and XY chains up to ten spins. The results show that by introducing two boundary impurities, one can obtain maximum entanglement at the limit of the impurity parameter |J1| ≪ J for the even-number qubits. When |J1/J| > 0, the entanglement always decreases with the increase in the absolute value of J1/J, and for the Heisenberg XXX chain, C disappears when J1/J exceeds a certain critical point Jic, and attains an asymptotic value C0 when |J1| ≫ J(J1 < 0), while for the Heisenberg XY chain, C always disappears when |J1/J| exceeds a certain critical point Jic. Both C0 and Jic decrease with the increase of the length of the chain.
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.