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

Progress of Theoretical Physics Supplement

Ground State Entanglement in Spin Systems

Hironori Yano, Hidetoshi Nishimori

Published Jan 1, 2005• 8 citations
Publisher

Abstract

We study the entanglement between arbitrary two spins in the XY and the antiferromagnetic Heisenberg spin chains in a uniform magnetic field.The entanglement of pairwise qubits in these models is obtained as a function of magnetic field by exact and numerical calculations.We find that the behavior of entanglement in the isotropic XY model is qualitatively the same as that in the Heisenberg model.Properties of entanglement length are also discussed.

DOI
10.1143/ptps.157.164

Related papers

Thermal and ground-state entanglement in the two-qubit anisotropic Heisenberg XY spin chain under an inhomogeneous magnetic field

D. Tian

We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

Entanglement in the Heisenberg XY Spin Ring Chain with Uniform External Magnetic Fields

Wanqiang Cao

The entanglement properties in the four-qubit Heisenberg XY model in the presence of an external uniform magnetic field are investigated.The analytic representation for the measures of entanglement are obtained.The effects of the anisotropic parameter on the thermal entanglement are discussed.

Journal of Yanbian University•Jan 1, 2009•0 citations

ENTANGLEMENT IN THE XY SPIN CHAIN WITH NONUNIFORM EXTERNAL MAGNETIC FIELDS

JUNPENG CAO, Z. Z. Sun, YIN SUN +2 more

We study the entanglement in the three-site Heisenberg XY model with nonuniform external magnetic fields and obtain analytic expressions for the measures of entanglement in the system with both the periodic and the open boundary conditions. We show that both the ground state and the excited states of the system possess remarkable entanglement properties and the entanglement clearly depends on the magnitude of external fields. We obtain the pairwise thermal entanglement of the system. We also discuss the boundary effects on the entanglement.

International Journal of Quantum Information•Sep 1, 2005•1 citation

ENTANGLEMENT IN THE XY HEISENBERG MODEL

Xin Tian, Jia-tih Lin, Liang Liu +1 more

We investigate the thermal entanglement of two-qubit anisotropic Heisenberg XY model in the presence of an external nonuniform magnetic field B along the z-axis. Concurrence, the measure of entanglement is calculated and its property is studied in different cases. Two best models, Ising model under a uniform magnetic and isotropic model in a nonuniform magnetic field, are discovered. In the two models, the critical temperature Tc (above which there is no entanglement) can be enhanced and its concurrence is maximal.

Modern Physics Letters B•Aug 30, 2004•4 citations

Entanglement and spin squeezing in the three-and four-qubit Heisenberg XY spin chain

Ming Hu

We investigate the pairwise entanglement and spin squeezing in the ground state of the three-and four-qubit Heisenberg XY spin chain and give analytical expressions of the concurrence C and the spin squeezing parameter ξ2.Our results show that the entanglement is equivalent to spin squeezing(i.e.the entanglement implies spin squeezing and vice versa)if the external magnetic field B is above a certain critical value Bc,where for the three-qubit case,Bc=J[(4-3γ2)1/2-1],and for the four-qubit case,Bc can be obtained numerically.

Journal of Atomic and Molecular Physics•Jan 1, 2008•0 citations

General Properties of Thermal Entanglement in an Arbitrary-Length Heisenberg Spin Chain

Ting Zhang, Wei Wu, Ping‐Xing Chen +1 more

We investigate general properties of thermal entanglement in arbitrary-length 1D Heisenberg spin-1/2 chain based on classifications of its eigenstates. The influences of magnetic field and temperature on entanglement are qualitatively discussed and three features are presented. The conclusions hold for both bipartite and multipartite entanglement, and are in agreement with the results numerically proven by Arnesen et al. [Phys. Rev. Lett. 59 (2001) 017901].

Chinese Physics Letters•Jul 26, 2007•1 citation
We study the entanglement between arbitrary two spins in the XY and the antiferromagnetic Heisenberg spin chains in a uniform magnetic field.The entanglement of pairwise qubits in these models is obtained as a function of magnetic field by exact and numerical calculations.We find that the behavior of entanglement in the isotropic XY model is qualitatively the same as that in the Heisenberg model.Properties of entanglement length are also discussed.
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.
We study the entanglement in the three-site Heisenberg XY model with nonuniform external magnetic fields and obtain analytic expressions for the measures of entanglement in the system with both the periodic and the open boundary conditions. We show that both the ground state and the excited states of the system possess remarkable entanglement properties and the entanglement clearly depends on the magnitude of external fields. We obtain the pairwise thermal entanglement of the system. We also discuss the boundary effects on the entanglement.
We investigate the thermal entanglement of two-qubit anisotropic Heisenberg XY model in the presence of an external nonuniform magnetic field B along the z-axis. Concurrence, the measure of entanglement is calculated and its property is studied in different cases. Two best models, Ising model under a uniform magnetic and isotropic model in a nonuniform magnetic field, are discovered. In the two models, the critical temperature Tc (above which there is no entanglement) can be enhanced and its concurrence is maximal.
We investigate the pairwise entanglement and spin squeezing in the ground state of the three-and four-qubit Heisenberg XY spin chain and give analytical expressions of the concurrence C and the spin squeezing parameter ξ2.Our results show that the entanglement is equivalent to spin squeezing(i.e.the entanglement implies spin squeezing and vice versa)if the external magnetic field B is above a certain critical value Bc,where for the three-qubit case,Bc=J[(4-3γ2)1/2-1],and for the four-qubit case,Bc can be obtained numerically.