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Journal of Physics A Mathematical and Theoretical

Entanglement in a periodic XX model with long-range interactions

Ming Zhong, Peiqing Tong

Published Aug 17, 2009• 1 citation
Publisher

Abstract

The nearest-neighbor concurrence and block–block entanglement of a period-two XX chain with a transverse field h and a uniform long-range interaction I in the z -direction are studied numerically. It is found that when I > 0, the nearest-neighbor concurrence and block–block entanglement are both discontinuous at the critical points, where the system undergoes first-order quantum phase transitions. When the long-range interaction is weak , there are two critical points and . Between these two points there is a critical region, where the block–block entanglement . In one noncritical region is equal to a non-zero constant while in the other noncritical region is always zero. Furthermore, the effect of periodicity on the concurrence and block–block entanglement is discussed.

DOI
10.1088/1751-8113/42/35/355002

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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.
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