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We study the entanglement properties in a one-dimensional Ising chain with a tilted magnetic field that is capable of showing both integrable and nonintegrable behaviors. Here the pairwise entanglement is characterized by concurrence and the multipartite entanglement is characterized by the Q measure. According to the entanglement properties of the ground state in the Ising mode, which have tilt angle, we can find that the Q measure decreases with the increasing of the strength of external field. And the phase transition property of the system is changed with the increase of tilt angle for the external magnetic field. We also consider the evolution of entanglement in this model, and find that the nonintegrability can suppress the pairwise entanglement but promotes the multipartite entanglement with the integrable system.
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Keywords:
- Ising model /
- nonintegrability /
- pairwise entanglement /
- multipartite entanglement
[1] Lakshminarayan A, Subrahmanyam V 2003 Phys. Rev. A 67 052304
[2] Gu B J, Ye B, Xu W B 2008 Acta Phys. Sin. 57 695 (in Chinese) [顾斌杰, 叶宾, 须文波 2008 物理学报 57 695]
[3] Ye B, Gu R J, Xu W B 2007 Acta Phys. Sin. 56 3718 (in Chinese) [叶宾, 谷瑞军, 须文波 2007 物理学报 56 3718]
[4] Scott A J, Caves C 2003 J. Phys. A 36 9553
[5] Wang X, Ghose S, Sanders B C, Hu B 2004 Phys. Rev. E 70 016217
[6] Santos L F, Rigolin G, Escobar C O 2004 Phys. Rev. A 69 042304
[7] Lakshminarayan A, Subrahmanyam V 2005 Phys. Rev. A 71 062334
[8] Song L J, Yan D, Gai Y J, Wang Y B 2011 Acta Phys. Sin. 60 020302 (in Chinese) [宋立军, 严冬, 盖永杰, 王玉波 2011 物理学报 60 020302]
[9] Wang X Q, Ma J, Zhang X H, Wang X G 2011 Chin. Phys. B 20 050510
[10] Wang X Q, Ma J, Song L J, Zhang X H, Wang X G 2010 Phys. Rev. E 82 056205
[11] Qin M 2010 Acta Phys. Sin. 59 2216 (in Chinese) [秦猛 2010 物理学报 59 2216]
[12] Yang Y, Wang A M 2013 Acta Phys. Sin. 62 130305 (in Chinese) [杨阳, 王安民 2013 物理学报 62 130305]
[13] Karthik J, Sharma A, Lakshminarayan A 2007 Phys. Rev. A 75 022304
[14] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[15] Meyer D A, Wallach N R 2002 J. Math. Phys. 43 4273
[16] Scott A J 2004 Phys. Rev. A 69 052330
[17] Brennen G K 2003 Quantum Information and Computation (Vol. 3) (Berlin: Springer) pp619–626
[18] Castro C S, Sarandy M S 2011 Phys. Rev. A 83 042334
[19] Jordan P, Wigner E 1928 Z. Phys. 47 631
[20] Sachdev S 1999 Quantum Phase Transitions (London: Cambridge University Press) p46
[21] Ma Z H, Chen Z H, Chen J L 2011 Phys. Rev. A 83 062325
[22] Chen J L, Deng D L, Su H Y, Wu C F, Oh C H 2011 Phys. Rev. A 83 022316
[23] Deng D L, Gu S J, Chen J L 2010 Annals Phys. 325 367
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[1] Lakshminarayan A, Subrahmanyam V 2003 Phys. Rev. A 67 052304
[2] Gu B J, Ye B, Xu W B 2008 Acta Phys. Sin. 57 695 (in Chinese) [顾斌杰, 叶宾, 须文波 2008 物理学报 57 695]
[3] Ye B, Gu R J, Xu W B 2007 Acta Phys. Sin. 56 3718 (in Chinese) [叶宾, 谷瑞军, 须文波 2007 物理学报 56 3718]
[4] Scott A J, Caves C 2003 J. Phys. A 36 9553
[5] Wang X, Ghose S, Sanders B C, Hu B 2004 Phys. Rev. E 70 016217
[6] Santos L F, Rigolin G, Escobar C O 2004 Phys. Rev. A 69 042304
[7] Lakshminarayan A, Subrahmanyam V 2005 Phys. Rev. A 71 062334
[8] Song L J, Yan D, Gai Y J, Wang Y B 2011 Acta Phys. Sin. 60 020302 (in Chinese) [宋立军, 严冬, 盖永杰, 王玉波 2011 物理学报 60 020302]
[9] Wang X Q, Ma J, Zhang X H, Wang X G 2011 Chin. Phys. B 20 050510
[10] Wang X Q, Ma J, Song L J, Zhang X H, Wang X G 2010 Phys. Rev. E 82 056205
[11] Qin M 2010 Acta Phys. Sin. 59 2216 (in Chinese) [秦猛 2010 物理学报 59 2216]
[12] Yang Y, Wang A M 2013 Acta Phys. Sin. 62 130305 (in Chinese) [杨阳, 王安民 2013 物理学报 62 130305]
[13] Karthik J, Sharma A, Lakshminarayan A 2007 Phys. Rev. A 75 022304
[14] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[15] Meyer D A, Wallach N R 2002 J. Math. Phys. 43 4273
[16] Scott A J 2004 Phys. Rev. A 69 052330
[17] Brennen G K 2003 Quantum Information and Computation (Vol. 3) (Berlin: Springer) pp619–626
[18] Castro C S, Sarandy M S 2011 Phys. Rev. A 83 042334
[19] Jordan P, Wigner E 1928 Z. Phys. 47 631
[20] Sachdev S 1999 Quantum Phase Transitions (London: Cambridge University Press) p46
[21] Ma Z H, Chen Z H, Chen J L 2011 Phys. Rev. A 83 062325
[22] Chen J L, Deng D L, Su H Y, Wu C F, Oh C H 2011 Phys. Rev. A 83 022316
[23] Deng D L, Gu S J, Chen J L 2010 Annals Phys. 325 367
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