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

arXiv:quant-ph/0105075 · Journal of Physics A Mathematical and General

Thermal entanglement in three-qubit Heisenberg models

Xiaoguang Wang, Hongchen Fu, A. I. Solomon

Published Dec 19, 2001• 144 citations
arXivHTMLPDF

Abstract

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic XXZ model, and the ferromagnetic XXZ model with anisotropy parameter Δ⩾1. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the uniform magnetic field can induce entanglement in the antiferromagnetic XXX model, but cannot induce entanglement in the ferromagnetic XXX model.

DOI
10.1088/0305-4470/34/50/312

Related papers

Thermal entanglement in three-qubit Heisenberg models

Wang, X, Fu, H, A. I. Solomon

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic XXZ model, and the ferromagnetic XXZ model with anisotropy parameter Δ≥1. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the uniform magnetic field can induce entanglement in the antiferromagnetic XXX model, but cannot induce entanglement in the ferromagnetic XXX model.

•May 16, 2001•108 citations

THREE-QUBITS GROUND STATE AND THERMAL ENTANGLEMENT OF ANISOTROPIC HEISENBERG (XXZ) AND ISING MODELS WITH DZYALOSHINSKII-MORIYA INTERACTION

Rouhollah Jafari, A. Langari

We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubits system. We have considered the anisotropic Heisenberg (XXZ) model in the presence of Dzyaloshinskii–Moriya (DM) interaction in addition to the Ising model in a magnetic field with DM interaction. We have found that the increment of DM interaction and magnetic field can enhance and reduce the entanglement of the system. We have shown that the non-symmetric pairwise state has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise one. For the negative anisotropy, the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy, it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in detail. The most remarkable result appears at zero temperature where the three-qubits ground state entanglement of the system (in spite of two-qubits counterpart) shows the fingerprint of the quantum phase transition for a system of infinite number of qubits.

International Journal of Quantum Information•Jun 1, 2011•25 citations

Thermal entanglement in the Heisenberg XXZ model under an inhomogeneous magnetic field

WU Ke-dong

We study the thermal entanglement in the two-qubit anisotropic XXZ model in the presence of an external inhomogeneous magnetic field along the z axis.Concurrence,the measurement of entanglement,is calculated.The effects of the anisotropic parameter Δ on the thermal entanglement are studied carefully for both the antiferromagnetic and ferromagnetic cases.The critical temperature Tc can also be controlled by the anisotropic parameter Δ.

Journal of Guizhou Normal University•Jan 1, 2009•0 citations

Three-Qubit Ground State and Thermal Entanglement of $XXZ$ Model With Dzyaloshinskii-Moriya Interaction

Rouhollah Jafari, A. Langari

We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.

arXiv:0903.2556•Mar 14, 2009•0 citations

Ground-State and Thermal Entanglement in Three-Spin Heisenberg- XXZ Chain with Three-Spin Interaction

Yong Zhang, Long Gui-Lu

The entanglement properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.

Communications in Theoretical Physics•Aug 1, 2007•8 citations

Pairwise entanglement in three-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction

Yanhui Wang, Yun‐Jie Xia, 山东省激光偏光与信息技术重点实验室，曲阜师范大学物理系，曲阜 273165

In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.

Acta Physica Sinica•Jan 1, 2009•7 citations
We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic XXZ model, and the ferromagnetic XXZ model with anisotropy parameter Δ⩾1. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the uniform magnetic field can induce entanglement in the antiferromagnetic XXX model, but cannot induce entanglement in the ferromagnetic XXX model.
We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic XXZ model, and the ferromagnetic XXZ model with anisotropy parameter Δ≥1. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the uniform magnetic field can induce entanglement in the antiferromagnetic XXX model, but cannot induce entanglement in the ferromagnetic XXX model.
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubits system. We have considered the anisotropic Heisenberg (XXZ) model in the presence of Dzyaloshinskii–Moriya (DM) interaction in addition to the Ising model in a magnetic field with DM interaction. We have found that the increment of DM interaction and magnetic field can enhance and reduce the entanglement of the system. We have shown that the non-symmetric pairwise state has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise one. For the negative anisotropy, the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy, it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in detail. The most remarkable result appears at zero temperature where the three-qubits ground state entanglement of the system (in spite of two-qubits counterpart) shows the fingerprint of the quantum phase transition for a system of infinite number of qubits.
Three-Qubit Ground State and Thermal Entanglement of XXZXXZXXZ Model With Dzyaloshinskii-Moriya Interaction
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubit anisotropic Heisenberg (XXZ) and Ising in a magnetic field models and in the presence of Dzyaloshinskii-Moriya (DM) interaction. We have found that increasing of the DM interaction and magnetic field can enhance and reduce the entanglement of system. We have shown that the non-symmetric pairwise has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise. For negative anisotropy the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in details. The most remarkable result happens at zero temperature where 3-qubit ground state entanglement of the system (in spite of 2-qubit counterpart) shows the fingerprint of quantum phase transition for an infinite size system.
The entanglement properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.