Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Multipartite Entanglement in Heisenberg Model

Jie Ren, Zhu Shi-Qun

Published Jun 1, 2008• 0 citations
Publisher

Abstract

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ = ±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.

DOI
10.1088/0253-6102/49/6/21

Related papers

Anisotropy and Magnetic Field Effects on the Entanglement of a Two Qubit Heisenberg XY Chain

G. Lagmago Kamta, Anthony F. Starace

We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature T(c) that is independent of the external B field.

Physical Review Letters•Feb 26, 2002•335 citations

Anisotropy and Magnetic Field Effects on the Genuine Multipartite Entanglement of Multi-Qubit Heisenberg {\it XY} Chains

Chang Chi Kwong, Ye Yeo

It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {\em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this characteristic behavior. Here, we first study the effect of anisotropy and magnetic field on the multipartite thermal entanglement of a four-qubit Heisenberg XY chain using the MKB concurrences. We show that this model exhibits characteristic behavior similar to that of the two-qubit model. In addition, we show that this can again be understood using the same mathematical property. Next, we show that the six-qubit Heisenberg XY chain possesses properties necessary for it to have the characteristic behavior too. Most importantly, it is possible to directly measure the multipartite MKB concurrences of pure states. This may provide an experimental verification of our conjecture that for a Heisenberg XY chain of any even number of qubits, it is always possible to obtain non-zero genuine multipartite entanglement at any finite temperature by applying a sufficiently large magnetic field.

arXiv:0704.1368•Apr 11, 2007•0 citations

Negativity of Heisenberg XY Model

Siping Liu

Using a universal entanglement measure,negativity,we investigate the thermal entanglement of two-qubit Heisenberg XY model in thermal equilibrium at temperature T in the presence of an external magnetic field B.When anisotropy parameter γ is large enough there occurs a revival of the entanglement.By adjusting the magnetic field B,one can produce entanglement for any finite T.For isotropic case there is no entanglement above a critical temperature that is independent of the external B field.

•Jan 1, 2010•0 citations

Anisotropy and Magnetic Field Effects on Entanglement of a Two-Spin (1/2,1) Mixed-Spin Heisenberg XY Chain

Wang Fei, Liping Fu, Ke-Tao Guo

We study the entanglement in anisotropic (1/2,1) mixed-spin Heisenberg XY model under the presence of an external magnetic field at thermal equilibrium. By adjusting the anisotropic parameter and the magnetic field, one is able to obtain entanglement at higher temperature. We find the evidence of the quantum phase transition in the model and observe that the quantum phase transition point at low temperature moves toward weak magnetic field with the increase of the anisotropic parameter.

Communications in Theoretical Physics•Aug 1, 2008•9 citations

Thermal Entanglement of a Two-Qubit Heisenberg XYZ Chain

Min Cao

Thermal entanglement of a two-qubit Heisenberg XYZ chain is studied.It is found that the ground state entanglement maintains a maximal constant until it drops suddenly at a critical magnetic field.Increasing the value of can extend the entanglement region in terms of temperature and magnetic field.At a finite temperature,increasing the anisotropy parameter can enhance and extend the revival entanglement when the magnetic field is beyond the critical point.These results may provide theoretical proof for manipulating the entanglement with magnetic field,strength of interaction and anisotropy parameter.

Journal of Nantong University•Jan 1, 2008•0 citations

Multipartite Entanglement of a Tetrahedron Lattice

Rong Zhang, Zhu Shi-Qun, Hao Xiang

Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C 4 . The concurrence C and multipartite entanglement C 4 depend on different coupling strengths J i and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J 1 when J 2 is negative while the multipartite entanglement C 4 is symmetric about J 1 when J 2 <2. For a regular tetrahedron lattice, the concurrence C of ground state is 1/3 for ferromagnetic case while C = 0 for antiferromagnetic case. However, there is no multipartite entanglement since C 4 = 0 in a regular tetrahedron lattice. The external magnetic field B can increase the maximum value of the concurrence C B and induce two or three peaks in C B . There is a peak in the multipartite entanglement C 4 B when C 4 B is varied as a function of the temperature T . This peak is mainly induced by the magnetic field B .

Communications in Theoretical Physics•Nov 1, 2006•1 citation
The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ = ±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.
We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature T(c) that is independent of the external B field.
It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {\em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this characteristic behavior. Here, we first study the effect of anisotropy and magnetic field on the multipartite thermal entanglement of a four-qubit Heisenberg XY chain using the MKB concurrences. We show that this model exhibits characteristic behavior similar to that of the two-qubit model. In addition, we show that this can again be understood using the same mathematical property. Next, we show that the six-qubit Heisenberg XY chain possesses properties necessary for it to have the characteristic behavior too. Most importantly, it is possible to directly measure the multipartite MKB concurrences of pure states. This may provide an experimental verification of our conjecture that for a Heisenberg XY chain of any even number of qubits, it is always possible to obtain non-zero genuine multipartite entanglement at any finite temperature by applying a sufficiently large magnetic field.
Thermal entanglement of a two-qubit Heisenberg XYZ chain is studied.It is found that the ground state entanglement maintains a maximal constant until it drops suddenly at a critical magnetic field.Increasing the value of can extend the entanglement region in terms of temperature and magnetic field.At a finite temperature,increasing the anisotropy parameter can enhance and extend the revival entanglement when the magnetic field is beyond the critical point.These results may provide theoretical proof for manipulating the entanglement with magnetic field,strength of interaction and anisotropy parameter.
Three-dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence C and 4-concurrence C 4 . The concurrence C and multipartite entanglement C 4 depend on different coupling strengths J i and are decreased when the temperature T is increased. For a symmetric tetrahedron lattice, the concurrence C is symmetric about J 1 when J 2 is negative while the multipartite entanglement C 4 is symmetric about J 1 when J 2 <2. For a regular tetrahedron lattice, the concurrence C of ground state is 1/3 for ferromagnetic case while C = 0 for antiferromagnetic case. However, there is no multipartite entanglement since C 4 = 0 in a regular tetrahedron lattice. The external magnetic field B can increase the maximum value of the concurrence C B and induce two or three peaks in C B . There is a peak in the multipartite entanglement C 4 B when C 4 B is varied as a function of the temperature T . This peak is mainly induced by the magnetic field B .