相互作用突然开启后的反铁磁海森伯模型

周宗立; 章国顺; 娄平

doi:10.7498/aps.60.031101

摘要

本文以反铁磁海森伯模型为对象,设想了一个相互作用在t=0时刻开启的非平衡体系.在低温近似下,本文利用重整化群流方程方法讨论了该体系可观测量随时间的演化趋势.本文根据此类体系的特点,给出了获得算符时间演化形式的路径,并成功将其应用于本文所讨论的模型中.其中,本文着重介绍了如何在非平衡自旋体系中应用流方程方法,并利用该方法得到了随时间演化的基态磁化强度,同时论证了该方法处理此类系统的有效性.同时,在与平衡体系基态磁化强度的对比中,发现非平衡可观测量随时间震荡而无法收敛,这一点有别于相互作用突然开

关键词:

Abstract

Based on the Heisenberg model, the anti-ferromagnet following the interaction suddenly switched-on at t=0 is considered in this paper. In the limit of low temperature, the time evolution of observables is analytically studied by utilizing the flow equation method. According to the unique feature of the system, the way to obtain the evolution of observables is shown and applied to the system we focused on. Further, special emphasis is laid on the application of the flow equation method to non-equilibrium magnetic systems so that the validity of the method applied to this kind of systems is traced. By means of this method, the evolution of magnetization of the ground state is traced in detail. It is found that the magnetization oscillates with time rather than converges,which is different from that of non-equilibrium Luttinger liquids.

Keywords:

作者及机构信息

(1)安徽大学物理与材料科学学院,合肥 230039; (2)安徽农业大学理学院,合肥 230036

基金项目: 安徽高校省级自然科学研究重点项目(批准号:KJ2010A123)资助的课题.

Authors and contacts

(1)School of Physics & Material Science, Anhui University, Hefei 230039, China; (2)School of Science, Anhui Agricultural University, Hefei 230036, China

参考文献

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[26]	Zhang K C, Liu B G 2009 Chin. Phys. B 18 3960
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施引文献

[1]	Stamper-Kurn D M, Miesner H J, Chikkatur A P, lnouye S, Stenger J, Ketterle W 1999 Phys. Rev. Lett. 83 661
[2]	Wu H Y, Yin L 2006 Acta Phys. Sin. 55 490 (in Chinese) [武宏宇、尹澜 2006 物理学报 55 490]
[3]	He Z M, Wang D L, Zhang W X, Wang F J 2008 Chin. Phys. B 17 3640
[4]	Chin C, Vuleti’c V, Kerman A J, Chu S 2001 Phys. Rev. Lett. 85 2717
[5]	Loftus T, Regal C A, Ticknor C, Bohn J L, Jin D S 2002 Phys. Rev. Lett. 88 173201
[6]	Greiner M, Mandel O, Esslinger T, Hnsch T W, Bloch I 2002 Nature 415 39
[7]	Barouch E, McCoy B 1970 Phys. Rev. A 2 1075
[8]	Stoferle T, Moritz H, Schori C, Kohl M, Esslinger T 2004 Phys. Rev. Lett. 92 130403
[9]	Fertig C D, O’Hara K M, Huckans J H, Rolston S L, Phillips W D, Porto J V 2005 Phys. Rev. Lett. 94 120403
[10]	Kinoshita T, Wenger T, Weiss D S 2006 Nature 440 900
[11]	Zhao J M, Zhang L J, Li C Y, Jia S T 2008 Acta Phys. Sin. 57 2895 (in Chinese) [赵建明、张临杰、李昌勇、贾锁堂 2008 物理学报 57 2895]
[12]	Schreck F Khaykovivh L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, Salomon C 2001 Phys. Rev. Lett. 87 080403
[13]	Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[14]	Jiang Y R, Feng M, Gao K L, Zhu X W 2001 Chin. Phys. 10 202
[15]	Calabrese P, Cardy J 2007 J. Stat. Mech. p06008
[16]	Wegner F 1994 Ann. Phys. 3 77
[17]	Glazek S D, Wilson K G 1994 Phys. Rev. D 49 4214
[18]	Kehrein S 2006 The Flow Equation Approach to Many-Particle Systems (Berlin: Springer) p98
[19]	Wang F, Zhang F S, Eric S 2003 Chin. Phys. 12 164
[20]	Cazalilla M A 2006 Phys. Rev. Lett. 97 156403
[21]	Moeckel M, Kehrein S 2008 Phys. Rev. Lett. 100 175702
[22]	Perfetto E 2006 Phys. Rev. B 74 205123
[23]	Dobrescu B E, Pokrovsky V L 2006 Phys. lett. A 350 154
[24]	Luo X L, Zhang Z F, Feng M, Fang X M, Gao K L, Zhu X W 1999 Acta Phys. Sin. 48 218 (in Chinese) [罗学立、张志飞、冯芒、方细明、高克林、朱熙文 1999 物理学报 48 218]
[25]	Cherng R W, Levitov L S 2006 Phys. Rev. A 73 043614
[26]	Zhang K C, Liu B G 2009 Chin. Phys. B 18 3960
[27]	Altman E, Auerbach A 2006 Phys. Rev. Lett. 89 250404
[28]	Hackl A, Kehrein S 2008 Phys. Rev. B 78 092303
[29]	Hackl A, Kehrein S 2009 J. Phys.: Condens. Matter 21 015601
[30]	Stenger J, Inouye S, Stamper-Kum D M, Miesner H J, Chikkatur A P, Ketterle W 1998 Nature 396 345
[31]	Chang M S, Hamley C D, Barrett M D, Saner J A, Fortier K M, Zhang W, You L, Chapman M S 2004 Phy. Rev. Lett. 92 140403
[32]	Zhao X D, Xie Z W, Zhang W P 2007 Acta Phys. Sin. 56 5358 (in Chinese) [赵兴东、谢征微、张卫平 2007 物理学报 56 5358]
[33]	Zheng G P, Liang J Q, Liu W M 2006 Ann. Phys. 321 950
[34]	Wang Y J, Liu X F, Han J R 2009 Chin. Phys. B 18 5301
[35]	Stein J, 1998, Eur Phys. J. B 5 193
[36]	Wang H, Lou P, Zhang Y H 2005 Acta Phys. Sin. 54 3764 (in Chinese) [汪洪、娄平、庄永河 2005 物理学报 54 3764]
[37]	Wang H, Lou P, Zhang Y H 2004 Acta Phys. Sin. 53 577 (in Chinese) [汪洪、娄平、庄永河 2004 物理学报 53 577]
[38]	Haldane F D M 1981 J. Phys. C 14 2585
[39]	Luther A, Peschel I 1974 Phys. Rev. B 9 2911

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