横场中非束缚类准周期伊辛链的赝临界点

张振俊; 李文娟; 朱璇; 熊烨; 童培庆

doi:10.7498/aps.64.190501

摘要

本文系统地研究了有限尺寸下非束缚类准周期量子伊辛链在横场中的赝临界点的行为. 首先, 通过计算平均磁矩和协作参量, 发现这两个量的导数随着横场的变化都会出现两个清晰的峰. 这与束缚类伊辛链和无序伊辛链的结果明显不同. 其次, 研究了横场中赝临界点的概率分布情况, 发现概率分布并不是高斯型的. 这也与无序的结果不同. 最后, 分析了赝临界点产生的原因, 发现赝临界点是由非束缚类准周期伊辛链中的集团结构造成的.

关键词:

Abstract

We study the quantum pseudocritical points in the unbounded quasiperiodic transverse field Ising chain of finite-size systematically. Firstly, we study the derivatives of averaged magnetic moment and the averaged concurrence with transverse fields. Both of them show two visible peaks, with are nearly not raised when the length of chain is increased. Moreover, the places where the peaks occur in the transverse field are obviously different from that of the quantum phase transition point in the thermodynamic limit. These results are very different from those of the bounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain. Then, we analyze the origin of the two visible peaks. For that we study the derivative of magnetic moment for each spin with transverse field. For all spins, the single magnetic moment only show one peak. However, the places where the peaks occur are not random. The peaks always occur in two regions. Thus, the derivatives of averaged magnetic moment reveal two peaks. Furthermore, we study the probability distribution of the pseudocritical points through finding out the peaks of the single magnetic moment in 1000 samples. The distribution is not Guassian. This result is obviously different from that of the disordered case. Besides, the pseudocritical points nearly do not occur at the quantum phase transition point. Finally, we analyze the origin of the pseudocritical points. For that we study the relationship between the spin places and the corresponding places of pseudocritical points. It is found that the pseudocritical points are caused by the two groups that exist in the nearest neighboring interactions of the unbounded quasiperiodic structure. When a spin is in one group, this group will decide the probable place of the pseudocritical point. Through this study, we find that although the quantum phase transition behaviors of the unbounded quasiperiodic transverse field Ising chain and the disordered transverse field Ising chain belong to the same universal class in the thermodynamic limit, the thermodynamic behaviors of the two Ising chains are very different as in finite sizes. The differences are caused by the special structure in the unbounded quasiperiodic system.

Keywords:

作者及机构信息

1.
河海大学理学院, 南京 210098;

2.
长沙师范学院初等教育系, 长沙 410100;

3.
江苏建康职业学院基础部, 南京 210029;

4.
南京师范大学物理科学与技术学院, 南京 210023;

5.
江苏省“大规模复杂系统数值模拟”重点实验室, 南京 210023

通信作者: 张振俊, hi_zhangzhenjun@sina.com;pqtong@njnu.edu.cn ; 童培庆, hi_zhangzhenjun@sina.com;pqtong@njnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11175087, 11305045)、湖南省自然科学基金(批准号: 2015JJ6006)和中央高校基本科研业务费(批准号: 2013B00414)资助的课题.

Authors and contacts

1.
College of Science, Hohai University, Nanjing 210098, China;

2.
Primary Education Department, Changsha Normal University, Changsha 410100, China;

3.
Department of Basic Courses , Jiangsu Jiankang Vocational College, Nanjing 210029, China;

4.
School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China;

5.
Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China

Corresponding author: Zhang Zhen-Jun, hi_zhangzhenjun@sina.com;pqtong@njnu.edu.cn ; Tong Pei-Qing, hi_zhangzhenjun@sina.com;pqtong@njnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China(Grant Nos.11175087,11305045), the National Science Foundation of Hunan Province of China(Grant No.2015JJ6006), and the Fundamental Research Funds for the Central Universities of China (Grant No. 2013B00414).

参考文献

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[3]	Grenier M, Mandel O, Esslinger T, Hnsch and Bloch I 2002 Nature 415 39
[4]	Vojta M 2003 Rep. Prog. Phys. 66 2069
[5]	Wang W G, Qin P Q, He L W, Wang P 2010 Phys. Rev. E 81 016214
[6]	Igli F, Lin Y-C, Rieger H, Monthus C 2007 Phys. Rev. B 76 064421
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[8]	Levine D, Steinhardt P 1984 Phys. Rev. Lett. 53 2477
[9]	Merlin R, Bajema K, Clarke R, Juang F Y, Bhattacharya P K 1985 Phys. Rev. Lett. 55 1768
[10]	St A 1987 Commun. Math. Phys. 111 409
[11]	Gumbs G, Ali M K 1988 Phys. Rev. Lett. 60 1081
[12]	Holzer M 1988 Phys. Rev. B 38 5756
[13]	Severin M, Riklund R 1989 Phys. Rev. B 39 10362
[14]	Chakrabarti A, Karmakar S N 1991 Phys. Rev. B 44 896
[15]	Godrche C, Luck J M 1992 Phys. Rev. B 45 176
[16]	Oh G Y, Lee M H 1993 Phys. Rev. B 48 12465
[17]	Doria M, Satija I 1988 Phys. Rev. Lett. 60 444
[18]	Benza V G 1989 Europhys. Lett. 8 321
[19]	Luck J M 1993 J. Stat. Phys. 72 417
[20]	Grimm U, Baake M 1994 J. Stat. Phys. 74 1233
[21]	Hrmisson J, Grimm U, Baake M 1997 J. Phys. A 30 7315
[22]	Hrmisson J, Grimm U 1998 Phys. Rev. B 57 R673
[23]	Tong P Q, Zhong M 2002 Phys. Rev. B 65 064421
[24]	Tong P Q, Liu X X 2006 Phys. Rev. Lett. 97 017201
[25]	Wotters W 1998 Phys. Rev. Lett. 80 2245
[26]	Pfeuty P 1979 Phys. Lett. A 72 245
[27]	Jordan P, Wigner E 1928 Z. Physik 47 631
[28]	Arnesen M, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[29]	Gringrich R and Adami C 2002 Phys. Rev. Lett. 89 270402
[30]	Osterloh A, Amico L, Falci G, Fazio R 2002 Nature 416 608
[31]	Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[32]	Wu L, Sarandy M S, Lidar D A 2004 Phys. Rev. Lett. 93 250404
[33]	Gu S, Deng S, Li Y, Lin H 2004 Phys. Rev. Lett. 93 086402
[34]	Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517
[35]	Gong L Y, Tong P Q 2008 Phys. Rev. B 78 115114
[36]	Zhu X, Tong P Q 2008 Chin. Phys. B 17 1623
[37]	Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 0531(in Chinese) [张松俊, 蒋建军, 刘拥军 2008 57 0531]
[38]	Wang P, Zheng Q, Wang W G 2010 Chin. Phys. Lett. 27 080301
[39]	Wang L C, Shen J, and Yi X X 2011 Chin. Phys. B 20 050306
[40]	Osborne T, Nielsen M 2002 Phys. Rev. A 66 032110

施引文献

[1]	Imada M, Fujimori A, Tokura Y 1998 Rev. Mod. Phys. 70 1039
[2]	Sachdev S 1999 Quantum Phase Transitions (Cambridge University Press, England)
[3]	Grenier M, Mandel O, Esslinger T, Hnsch and Bloch I 2002 Nature 415 39
[4]	Vojta M 2003 Rep. Prog. Phys. 66 2069
[5]	Wang W G, Qin P Q, He L W, Wang P 2010 Phys. Rev. E 81 016214
[6]	Igli F, Lin Y-C, Rieger H, Monthus C 2007 Phys. Rev. B 76 064421
[7]	Shechtman D, Blech I, Gratias D, Cahn J W 1984 Phys. Rev. Lett. 53 1951
[8]	Levine D, Steinhardt P 1984 Phys. Rev. Lett. 53 2477
[9]	Merlin R, Bajema K, Clarke R, Juang F Y, Bhattacharya P K 1985 Phys. Rev. Lett. 55 1768
[10]	St A 1987 Commun. Math. Phys. 111 409
[11]	Gumbs G, Ali M K 1988 Phys. Rev. Lett. 60 1081
[12]	Holzer M 1988 Phys. Rev. B 38 5756
[13]	Severin M, Riklund R 1989 Phys. Rev. B 39 10362
[14]	Chakrabarti A, Karmakar S N 1991 Phys. Rev. B 44 896
[15]	Godrche C, Luck J M 1992 Phys. Rev. B 45 176
[16]	Oh G Y, Lee M H 1993 Phys. Rev. B 48 12465
[17]	Doria M, Satija I 1988 Phys. Rev. Lett. 60 444
[18]	Benza V G 1989 Europhys. Lett. 8 321
[19]	Luck J M 1993 J. Stat. Phys. 72 417
[20]	Grimm U, Baake M 1994 J. Stat. Phys. 74 1233
[21]	Hrmisson J, Grimm U, Baake M 1997 J. Phys. A 30 7315
[22]	Hrmisson J, Grimm U 1998 Phys. Rev. B 57 R673
[23]	Tong P Q, Zhong M 2002 Phys. Rev. B 65 064421
[24]	Tong P Q, Liu X X 2006 Phys. Rev. Lett. 97 017201
[25]	Wotters W 1998 Phys. Rev. Lett. 80 2245
[26]	Pfeuty P 1979 Phys. Lett. A 72 245
[27]	Jordan P, Wigner E 1928 Z. Physik 47 631
[28]	Arnesen M, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[29]	Gringrich R and Adami C 2002 Phys. Rev. Lett. 89 270402
[30]	Osterloh A, Amico L, Falci G, Fazio R 2002 Nature 416 608
[31]	Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[32]	Wu L, Sarandy M S, Lidar D A 2004 Phys. Rev. Lett. 93 250404
[33]	Gu S, Deng S, Li Y, Lin H 2004 Phys. Rev. Lett. 93 086402
[34]	Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517
[35]	Gong L Y, Tong P Q 2008 Phys. Rev. B 78 115114
[36]	Zhu X, Tong P Q 2008 Chin. Phys. B 17 1623
[37]	Zhang S J, Jiang J J, Liu Y J 2008 Acta Phys. Sin. 57 0531(in Chinese) [张松俊, 蒋建军, 刘拥军 2008 57 0531]
[38]	Wang P, Zheng Q, Wang W G 2010 Chin. Phys. Lett. 27 080301
[39]	Wang L C, Shen J, and Yi X X 2011 Chin. Phys. B 20 050306
[40]	Osborne T, Nielsen M 2002 Phys. Rev. A 66 032110

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