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Acta Physica Sinica

The entanglement between the boundary qubits in the five-qubit Heisenberg XX open chain

Xiao-Qiang Xi, Chen Wen-xue, Qi Liu, Rui‐Hong Yue, (1)西安邮电学院应用数学与应用物理系，西安 710061; (2)西北大学现代物理研究所，西安 710069

Published Jan 1, 2006• 16 citations
Publisher

Abstract

Heisenberg XX open chain is very important in the study of quantum state transition. In this paper, we calculate the entanglement between the boundary qubits in the five-qubit Heisenberg XX open chain. When introducing magnetic impurity and system impurity and they satisfy linear relation, the system can be solved exactly, and there exist entanglement between the boundary qubits. Choosing the magnetic and system impurity properly, the boundary entanglement can get the maximal value 0.5.

DOI
10.7498/aps.55.3026

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Heisenberg XX open chain is very important in the study of quantum state transition. In this paper, we calculate the entanglement between the boundary qubits in the five-qubit Heisenberg XX open chain. When introducing magnetic impurity and system impurity and they satisfy linear relation, the system can be solved exactly, and there exist entanglement between the boundary qubits. Choosing the magnetic and system impurity properly, the boundary entanglement can get the maximal value 0.5.
The pairwise entanglement in the four-qubit Heisenberg XX open chain with external magnetic fields is calculated,and the analytical expressions for the measures of entanglement Concurrence are obtained.It is found that the entanglement between the boundary qubits can reach the value of 0.28 in the system with uniform external magnetic fields.In addition,in the Heisenberg XX model with external magnetic fields on the two boundary qubits,the two non-boundary qubits will be in the maximal entanglement by increasing the magnetic field at low temperature.
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.
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.
We study entanglement of a pair of qubits and the bipartite entanglement between the pair and the rest within open-ended Heisenberg XXX and XY models. The open boundary condition leads to strong oscillations of entanglements with a two-site period, and the two kinds of entanglements are 180 degrees out of phase with each other. The mean pairwise entanglement and ground-state energy per site in the XXX model are found to be proportional to each other. We study the effects of a single bulk impurity on entanglement, and find that there exist threshold values of the relative coupling strength between the impurity and its nearest neighbors, after which the impurity becomes pairwise entangled with its nearest neighbors.
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.