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Chinese Physics C

Effects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain

Ming Hu

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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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Efiects of the Next-Nearest-Neighbor Interaction on the Entanglement of the Heisenberg XX Chain *

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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

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Thermal entanglement in a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction

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In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.

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Entanglement in the Mixed-three-spin $XXX$ Heisenberg Model with the Next-nearest-neighbour Interaction

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In this paper, we investigate thermal pairwise quantum correlation for any pair of spins of a mixed-three-spin XXX Heisenberg system (with spins connected together with the nearest-neighbour (NN) and that of the next-nearest-neighbour (NNN) coupling constants J 1 and J 2 ) by means of concurrence and quantum discord, as functions of temperature T , magnetic field B and the coupling constants J 2 and J 1 .Some comparisons between these measures of entanglement are done for next-nearest-neighbour spins.We also express some magnetic properties and discuss the behaviour of the system in some special critical points.Some interesting and novel discussions are done to introduce some entanglement witnesses.

Acta Physica Polonica B•Jan 1, 2015•8 citations
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.
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
The features of the concurrences between the nearest-neighbors and that of the next-nearest-neighbors for the one-dimensional Heisenberg model with next-nearest-neighbor coupling JJJ are studied as functions of temperature and JJJ. The two concurrences exhibit a different dependence on JJJ at the ground state, which could be interpreted from the point of view of the correlation functions. The threshold temperature at which the concurrence is zero and the temperature effect on the two concurrences for systems up to 12 sites are studied numerically.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
We investigate the effects of anisotropy on the dynamic evolution of pairwise entanglement in the four-qubit Heisenberg XXZ model. The entanglement between the nearest-neighbor and the next nearest-neighbor qubits are calculated by making use of concurrence. Our results show that the sudden death effect can be weakened when introducing the anisotropy Δ. In addition, we also find that the anisotropy Δ can protect the entanglement between the nearest-neighbor qubits from being completely destroyed by the intrinsic decoherence, but it cannot do this for the entanglement between the next nearest-neighbor qubits.
In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.
Entanglement in the Mixed-three-spin XXXXXXXXX Heisenberg Model with the Next-nearest-neighbour Interaction
In this paper, we investigate thermal pairwise quantum correlation for any pair of spins of a mixed-three-spin XXX Heisenberg system (with spins connected together with the nearest-neighbour (NN) and that of the next-nearest-neighbour (NNN) coupling constants J 1 and J 2 ) by means of concurrence and quantum discord, as functions of temperature T , magnetic field B and the coupling constants J 2 and J 1 .Some comparisons between these measures of entanglement are done for next-nearest-neighbour spins.We also express some magnetic properties and discuss the behaviour of the system in some special critical points.Some interesting and novel discussions are done to introduce some entanglement witnesses.