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Acta Physica Polonica B

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

Hamid Arian Zad

Published Jan 1, 2015• 8 citations
Publisher

Abstract

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.

DOI
10.5506/aphyspolb.46.1911

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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.
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.
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.
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
We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first-order quantum phase transitions by tuning two parameters, x and y, of the Hamiltonian to specific values. The three-qubit chain is open-ended so that there are two types of pairwise entanglement: nearest-neighbour (nn) and next-nearest-neighbour (nnn). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters x, y and the temperature T. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter x. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular Cr(7)Ni-Cu(2+)-Cr(7)Ni complex which serves as a three-qubit system at sufficiently low temperatures.
We study entanglement and discord in spin glass. By using the Edwards–Anderson XX model, we consider the Hamiltonian for three and four particles for nearest neighbor and next nearest neighbor interactions and to solve for the entanglement through concurrence. With a fixed mean and changing variances for the coupling J , the concurrence and discord are numerically plotted against the temperature. For J = 1, the critical temperature is found to be 2.106. The entanglement was found to increase beyond the critical temperature as the variance increases. The spin–spin correlation for three particles is plotted as a function of temperature T .