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[1] S. Sachdev: Quantum Phase Transition , Cambridge Uni- versity Press, Cambridge 1999. 

[2] M. Greiner et al ., Nature(London) 419 , 51 (2002); T. W. B. Kibble, J. Phys. A 9 , 1387 (1976); W. H. Zurek, Nature(London) 317 , 505 (1985). 

[3] K. Sengupta, S. Powell and S. Sachdev, Phys. Rev. A 69 , 053616 (2004). 

[4] W. H. Zurek, U. Dorner and P. Zoller, Phys. Rev. Lett. 95 , 105701 (2005). 

[5] J. Dziarmaga, Phys. Rev. Lett. 95 , 245701 (2005). 

[6] A. Polkovnikov, Phys. Rev. B 72 , 161201(R) (2005). 

[7] A. Sen, U. Sen and M. Lewenstein, Phys. Rev. A 72 ,052319 (2005). 

[8] B. Damski and W. H. Zurek, Phys. Rev. A 73 , 063405 (2006). 

[9] F. M. Cucchietti, B. Damski, J. Dziarmaga and W. H. Zurek, Phys. Rev. A 75 , 023603 (2007). 

[10] V. Mukherjee, U. Divakaran, A. Dutta and D. Sen, Phys. Rev. B 76 , 174303 (2007). 

[11] K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100 , 077204 (2008). 

[12] A. Polkovnikov and V. Gritsev, Nat. Phys. 4 , 477 (2008). 

[13] M. Rigol, V. Dunjko and M. Olshanii, Nature (London) 452 , 854 (2008). 

[14] Y. Li, M. Huo and Z. Song, Phys. Rev. B 80 , 054404 (2009). 

[15] M. Rigol et al ., Phys. Rev. Lett. 98 , 050405 (2007); M. Rigol et al ., Phys. Rev. A 74 , 053616 (2006). 

[16] D. Patane, A. Silva, F. Sols and L. Amico, Phys. Rev. Lett. 102 , 245701 (2009). 

[17] S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, J. Schmiedmayer, Nature 449 , 324 (2007). 

[18] G. Roux, Phys. Rev. A 79 , 021608(R) (2009). 

[19] E. Barouch, B. M. McCoy and M. Dresden, Phys. Rev. A 2 , 1075 (1970); E. Barouch and B. M. McCoy, Phys. Rev. A 3 , 786 (1971); E. Barouch and B. M. McCoy, Phys. Rev. A 3 , 2137 (1971). 

nomena of sudden quench and static system. The long- range correlation is also studied and we find that sudden quench can destroy long-range correlation in the x direc- tion. As we know, the one-spin reduced density matrix can always be written as ρ = ( I + ∑ α = $_{x,y,z}$〈 σ$_{α}$ 〉 σ$_{α}$ ) / 2. If considering symmetry breaking effects in XY chain [20], we cannot suppose 〈 σ$_{x}$ 〉 = 0. Therefore for static case it will be a complex task to solve 〈 σ$_{x}$ 〉 . But for sudden quench, 〈 σ$_{x}$ ( a, b ) 〉 = 0 for a ̸ = b . So our result can help to simplify the calculation of one (two)-site reduced density matrix. This will be useful in studying the entanglement of one site with others for XY model. In addition, the general conclusion can be useful for other quantities and other models. 

This work was supported by NSF of China un- der Grants No. 10821403 and No. 10974234, pro- grams of Chinese Academy of Sciences, 973 grant No. 2010CB922904 and National Program for Basic Research of MOST. 

[20] T. R. de Oliveira, G. Rigolin, M. C. de Oliveira and E. Miranda, Phys. Rev. A 77 , 032325 (2008). 

