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本文研究了两格点、三格点以及四格点混合自旋 (1/2, 1) XY系统的热纠缠, 通过数值计算, 探讨了纠缠随温度和外磁场的变化关系. 发现在外磁场不存在或比较弱的情况下,纠缠随着温度的升高单调减小. 对于两格点和四格点系统,不论是铁磁还是反铁磁情况, 纠缠都在同一临界温度下消失, 并且这一临界值不受外磁场变化的影响. 对于三格点系统,临界温度也不受外磁场的影响, 但是铁磁情况下系统的临界温度高于反铁磁情况. 在温度极低的环境中, 纠缠在一定的磁场范围内形成稳定的平台, 但是当磁场强度超过某一临界值时, 纠缠完全消失. 本文还对混合自旋和单一自旋系统的热纠缠进行了对比分析, 发现在混合自旋系统中存在多层次的能级交错现象.In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.
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Keywords:
- XY model /
- quantum entanglement /
- external magnetic field
[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Bell J S 1964 Physics 1 195
[3] Aspect A, Dalibard J, Roger G 1982 Phys. Rev. Lett. 49 1804
[4] Bose I, Chattopadhyay E 2002 Phys. Rev. A 66 062320
[5] Osborne T J, Nielsen M A 2002 Phys. Rev. A 66 032110
[6] Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[7] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[8] Zhou L, Song H S, Guo Y Q, Li C 2003 Phys. Rev. A 68 024301
[9] Abliz A, Gao H J, Xie X C, Wu Y S, Liu W M 2006 Phys. Rev. A 74 052105
[10] Wang X G 2001 Phys. Rev. A 64 012313
[11] Wang X G 2002 Phys. Rev. A 66 034302
[12] Kamta G L, Starace A F 2002 Phys. Rev. Lett. 88 107901
[13] Sun Y, Chen Y G, Chen H 2003 Phys. Rev. A 68 044301
[14] Its A R, Jin B Q, Korepin V E 2005 J. Phys. A: Math. Gen. 38 2975
[15] Zhang L F, Tong P Q 200 5J. Phys. A: Math. Gen. 38 7377
[16] Liu S X, Li S S, Kong X M 2011 Acta Phys. Sin. 60 030303 (in Chinese) [刘圣鑫, 李莎莎, 孔祥木 2011 物理学报 60 030303]
[17] Du X M, Man Z X, Xia Y J 2008 Acta Phys. Sin. 57 7462 (in Chinese) [杜秀梅, 满忠晓, 夏云杰 2008 物理学报 57 7462]
[18] Shan C J, Chen W W, liu T K, Huang Y X, Li H 2008 Acta Phys. Sin. 57 2687 (in Chinese) [单传家, 程维文, 刘堂昆, 黄燕霞, 李宏 2008 物理学报 57 2687]
[19] Peres A 1996 Phys. Rev. Lett. 77 1413
[20] Vidal G 2002 Phys. Rev. A 65 032314
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[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Bell J S 1964 Physics 1 195
[3] Aspect A, Dalibard J, Roger G 1982 Phys. Rev. Lett. 49 1804
[4] Bose I, Chattopadhyay E 2002 Phys. Rev. A 66 062320
[5] Osborne T J, Nielsen M A 2002 Phys. Rev. A 66 032110
[6] Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[7] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[8] Zhou L, Song H S, Guo Y Q, Li C 2003 Phys. Rev. A 68 024301
[9] Abliz A, Gao H J, Xie X C, Wu Y S, Liu W M 2006 Phys. Rev. A 74 052105
[10] Wang X G 2001 Phys. Rev. A 64 012313
[11] Wang X G 2002 Phys. Rev. A 66 034302
[12] Kamta G L, Starace A F 2002 Phys. Rev. Lett. 88 107901
[13] Sun Y, Chen Y G, Chen H 2003 Phys. Rev. A 68 044301
[14] Its A R, Jin B Q, Korepin V E 2005 J. Phys. A: Math. Gen. 38 2975
[15] Zhang L F, Tong P Q 200 5J. Phys. A: Math. Gen. 38 7377
[16] Liu S X, Li S S, Kong X M 2011 Acta Phys. Sin. 60 030303 (in Chinese) [刘圣鑫, 李莎莎, 孔祥木 2011 物理学报 60 030303]
[17] Du X M, Man Z X, Xia Y J 2008 Acta Phys. Sin. 57 7462 (in Chinese) [杜秀梅, 满忠晓, 夏云杰 2008 物理学报 57 7462]
[18] Shan C J, Chen W W, liu T K, Huang Y X, Li H 2008 Acta Phys. Sin. 57 2687 (in Chinese) [单传家, 程维文, 刘堂昆, 黄燕霞, 李宏 2008 物理学报 57 2687]
[19] Peres A 1996 Phys. Rev. Lett. 77 1413
[20] Vidal G 2002 Phys. Rev. A 65 032314
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