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

[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 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 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 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 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 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 53 577]
[38]	Haldane F D M 1981 J. Phys. C 14 2585
[39]	Luther A, Peschel I 1974 Phys. Rev. B 9 2911

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 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 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 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 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 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 53 577]
[38]	Haldane F D M 1981 J. Phys. C 14 2585
[39]	Luther A, Peschel I 1974 Phys. Rev. B 9 2911

[1]	李再东, 南雪萌, 屈川, 刘伍明. 飞秒尺度下的惯性磁化强度动力学. , 2023, 72(10): 107502. doi: 10.7498/aps.72.20230345
[2]	王日兴, 曾逸涵, 赵婧莉, 李连, 肖运昌. 自旋轨道矩协助自旋转移矩驱动磁化强度翻转. , 2023, 72(8): 087202. doi: 10.7498/aps.72.20222433
[3]	王伟, 揭泉林. 基于机器学习J₁-J₂反铁磁海森伯自旋链相变点的识别方法. , 2021, 70(23): 230701. doi: 10.7498/aps.70.20210711
[4]	李再东, 郭奇奇. 铁磁纳米线中磁化强度的磁怪波. , 2020, 69(1): 017501. doi: 10.7498/aps.69.20191352
[5]	郑伟, 杜安. 外场作用下铁电/铁磁双层膜的极化磁化性质. , 2019, 68(3): 037501. doi: 10.7498/aps.68.20181879
[6]	李晓杰, 刘中强, 王春阳, 徐玉良, 孔祥木. 双模随机晶场对纳米管上Blume-Capel模型磁化强度和相变的影响. , 2015, 64(24): 247501. doi: 10.7498/aps.64.247501
[7]	邵宗乾, 陈金望, 李玉奇, 潘孝胤. 限制在一维谐振势下的三维自由电子气的一些热力学性质. , 2014, 63(24): 240502. doi: 10.7498/aps.63.240502
[8]	蒋建军, 杨翠红, 刘拥军. 一种等效于反铁磁海森伯混合自旋链的铁磁-反铁磁交替自旋链. , 2012, 61(6): 067502. doi: 10.7498/aps.61.067502
[9]	成泰民, 葛崇员, 孙树生, 贾维烨, 李林, 朱林, 马琰铭. 自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争. , 2012, 61(18): 187502. doi: 10.7498/aps.61.187502
[10]	郭光华, 张光富, 王希光. 反铁磁耦合硬磁-软磁-硬磁三层膜体系的不可逆交换弹性反磁化过程. , 2011, 60(10): 107503. doi: 10.7498/aps.60.107503
[11]	陈杰, 鲁习文. 舰船感应磁场预测的一种新方法. , 2010, 59(1): 239-245. doi: 10.7498/aps.59.239
[12]	高鹏, 殷海荣, 宫玉彬, 杨中海, 魏彦玉. 考虑非常数自旋扭矩时LLS方程的微扰解. , 2010, 59(5): 3504-3508. doi: 10.7498/aps.59.3504
[13]	张继业, 骆军, 梁敬魁, 纪丽娜, 刘延辉, 李静波, 饶光辉. 赝二元固溶体TbGa1-xGex(0≤x≤0.4)的结构与磁性. , 2008, 57(10): 6482-6487. doi: 10.7498/aps.57.6482
[14]	王怀玉, 夏青. 海森伯铁磁系统的总能量. , 2007, 56(9): 5466-5470. doi: 10.7498/aps.56.5466
[15]	王泽温, 介万奇. 稀磁半导体Hg0.89Mn0.11Te磁化强度及磁化率的研究. , 2007, 56(2): 1141-1145. doi: 10.7498/aps.56.1141
[16]	金硕, 解炳昊. 外磁场中海森伯反铁磁模型的代数结构和压缩态解. , 2006, 55(8): 3880-3884. doi: 10.7498/aps.55.3880
[17]	肖春涛, 曹先胜. La0.67Pb0.33MnO3的Preisach分析. , 2004, 53(7): 2347-2351. doi: 10.7498/aps.53.2347
[18]	王维, 张锡娟, 杨翠红, 成海英. 强磁场下Er2Ga5O12的磁晶各向异性. , 2002, 51(12): 2846-2848. doi: 10.7498/aps.51.2846
[19]	沈保根, 詹文山, 赵见高, 陈金昌. 非晶态Fe87-xSixB13合金的磁化强度、电阻与温度的关系. , 1985, 34(8): 1009-1016. doi: 10.7498/aps.34.1009
[20]	罗河烈, 文亦汀, 孙克, 冯远冰, 黄锡成. 表面效应对γ-Fe2O3微粉饱和磁化强度的影响. , 1983, 32(6): 812-818. doi: 10.7498/aps.32.812

计量

文章访问数: 8941
PDF下载量: 873
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板