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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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