Abstract.
In this paper, we investigate the entanglement of a two-spin system with Heisenberg exchange interaction in a quantized field. The pairwise entanglement between bipartite subsystems is obtained. It is shown that the entanglement exhibits a quantum phase transition due to the variation of exchang coupling. Phase diagrams are obtained explicitly. The analogy of the quantum phase transition compared to the case under a classical field are addressed.
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References
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000)
C.H. Bennett, D.P. DiVincenzo, Nature 404, 247 (2000)
C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)
V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997)
V. Vedral, M.B. Plenio, Phys. Rev. A 57, 1619 (1998)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)
M.A. Nielson, Ph.D. thesis, University of New Mexico, 1998, arXiv:quant-ph/0011036
M.C. Arnesen, S. Bose, V. Vedral, Phys. Rev. Lett. 87, 017901 (2001)
X. Wang, Phys. Rev. A 64, 012313 (2001); X. Wang, Phys. Rev. A 66, 034302 (2002); X. Wang, Phys. Rev. A 66, 044305 (2002)
D. Gunlycke, V.M. Kendon, V. Vedral, S. Bose, Phys. Rev. A 64, 042302 (2001)
G. Lagmago Kamta, A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002)
Y. Sun, Y.G. Chen, H. Chen, Phys. Rev. A 68, 044301 (2003)
G.-F. Zhang et al., Eur. Phys. J. D 32, 409 (2005); G.-F. Zhang, S.-S. Li, Eur. Phys. J. D 37, 123 (2006)
J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, Phys. Rev. Lett. 44, 1323 (1980)
R. Loudon, P. Knight, J. Mod. Opt. 34, 709 (1987)
I. Fuentes-Guridi, A. Carollo, S. Bose, V. Vedral, Phys. Rev. Lett. 89, 220404 (2002)
A. Carollo, I. Fuentes-Guridi, M. Franca Santos, V. Vedral, Phys. Rev. A 67, 063804 (2003)
L.C. Wang, H.T. Cui, X.X. Li, Phys. Rev. A 70, 052106 (2004)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002)
R. Somma et al., Phys. Rev. A 70, 042311 (2004)
T. Roscilde et al., Phys. Rev. Lett. 93, 167203 (2004)
T. Roscilde et al., Phys. Rev. Lett. 94, 147208 (2005)
J. Reslen et al., Europhys. Lett. 69, 8 (2005)
L.-A. Wu et al., Phys. Rev. Lett. 93, 250404 (2004)
X. Peng, J. Du, D. Suter, Phys. Rev. A 71, 012307 (2005)
A. Osterloh et al., Nature 416, 608 (2002)
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He, MM., Xu, CT., Chen, G. et al. Quantum phase transition of entanglement in Heisenberg spin model with quantized field. Eur. Phys. J. D 39, 313–320 (2006). https://doi.org/10.1140/epjd/e2006-00087-1
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DOI: https://doi.org/10.1140/epjd/e2006-00087-1