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Journal of Atomic and Molecular Physics

Entanglement of the Heisenberg XXX spin chain under uniform and nonuniform magnetic fields

D. Tian

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

We study the nearest and next nearest neighbor entanglement of the Heisenberg XXX spin chain (antiferromagnet) under uniform and nonuniform magnetic fields up to 10 spins.At zero absolute temperature,we show that there are staircase structures in concurrence C,this may be used to construct a quantum entanglement amplifier or switch.For finite temperature,we show that when a nonuniform magnetic field Bi=(-1)iB is introduced,the nearest neighbor entanglement may be enhanced at certain regions of B and T,while the next nearest neighbor entanglement completely disappeared.The critical temperature Tcn at which the nearest neighbor entanglement vanishes is also improved by introducing the nonuniform magnetic field Bi=(-1)iB,Tcn increases with the increase of B,which means one can get entanglement at any temperature by adjusting the magnetic field strength.

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We study the nearest and next nearest neighbor entanglement of the Heisenberg XXX spin chain (antiferromagnet) under uniform and nonuniform magnetic fields up to 10 spins.At zero absolute temperature,we show that there are staircase structures in concurrence C,this may be used to construct a quantum entanglement amplifier or switch.For finite temperature,we show that when a nonuniform magnetic field Bi=(-1)iB is introduced,the nearest neighbor entanglement may be enhanced at certain regions of B and T,while the next nearest neighbor entanglement completely disappeared.The critical temperature Tcn at which the nearest neighbor entanglement vanishes is also improved by introducing the nonuniform magnetic field Bi=(-1)iB,Tcn increases with the increase of B,which means one can get entanglement at any temperature by adjusting the magnetic field strength.
The thermal entanglement of a three-qubit Heisenberg chain under a nonuniform magnetic field is studied. It is very interesting to note that the next nearest neighbor entanglement (NNNE) could be larger than the nearest neighbor entanglement (NNE). We analyze the ground state entanglement, and give the conditions that NNNE is larger than NNE near zero temperature. Our results also show that the nonuniform field could induce the entanglement and improve the threshold temperature at certain parameter region.
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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Abstract The pairwise entanglement of the Heisenberg XX chain with next-nearest-neighbor (NNN) interac-tions 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 jJj . The critical tempera-ture T c decreases with the increase of J for the nearest-neighbor entanglement and increases with the increaseof jJj for the next-nearest-neighbor entanglement, respectively. We also show that the general Heisenberg XXmodel still can be used to create the entangled W states of three and four qubits, and that the presence ofNNN coupling has no efiect on the creation of four-qubit W states, while it shifts the instant of time at whichthe three-qubit W states are created.Key words Heisenberg XX chain, next-nearest-neighbor interaction, thermal entanglement 1 Introduction
We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero temperature and in the uniform magnetic field at finite temperatures. We use the concurrence to quantify the entanglement. We find that, in the ferromagnetic region of the uniform magnetic field hhh, all the concurrences are \textit{generated} by the random magnetic field and by the thermal fluctuation. In one particular region of hhh, the next-nearest neighbor concurrence is generated by the random field but not at finite temperatures. We also find that the qualitative behavior of the maximum point of the entanglement in the random magnetic field depends on whether the variance of its distribution function is finite or not.
We investigate the entanglement property of a two-qubit, mixed-spin, Heisenberg system under a nonuniform magnetic field. We show that increasing b can improve the threshold temperature, and can also make the entanglement enhanced. It is very interesting to note that the joining of the nonuniform magnetic field b can not only induce the entanglement for the ferromagnetic case, but can also make the entanglement symmetrical in terms of J for a larger value of b , while the uniform field B cannot do this. We also analyze the ground-state entanglement features in detail.