Quantum information entropy for one-dimensional system undergoing quantum phase transition

doi:10.1088/1674-1056/25/5/050302

中国物理B ›› 2016, Vol. 25 ›› Issue (5): 50302-050302.doi: 10.1088/1674-1056/25/5/050302

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Xu-Dong Song(宋旭东), Shi-Hai Dong(董世海), Yu Zhang(张宇)

1. Software Institute, Dalian Jiaotong University, Dalian 116028, China;
2. CIDETEC, Instituto Politécnico Nacional, Unidad Profesional ALM, Mexico D. F. 07700, Mexico;
3. Department of Physics, Liaoning Normal University, Dalian 116029, China

收稿日期:2015-12-16 修回日期:2016-01-11 出版日期:2016-05-05 发布日期:2016-05-05
通讯作者: Yu Zhang E-mail:dlzhangyu_physics@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Xu-Dong Song(宋旭东)¹, Shi-Hai Dong(董世海)², Yu Zhang(张宇)³

1. Software Institute, Dalian Jiaotong University, Dalian 116028, China;
2. CIDETEC, Instituto Politécnico Nacional, Unidad Profesional ALM, Mexico D. F. 07700, Mexico;
3. Department of Physics, Liaoning Normal University, Dalian 116029, China

Received:2015-12-16 Revised:2016-01-11 Online:2016-05-05 Published:2016-05-05
Contact: Yu Zhang E-mail:dlzhangyu_physics@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.

摘要/Abstract

摘要： Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.

关键词: quantum information entropy, quantum phase transition, entropy uncertainty relation

Abstract: Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.

Key words: quantum information entropy, quantum phase transition, entropy uncertainty relation

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Ge (Solutions of wave equations: bound states) 03.67.-a (Quantum information)

宋旭东, 董世海, 张宇. Quantum information entropy for one-dimensional system undergoing quantum phase transition[J]. 中国物理B, 2016, 25(5): 50302-050302.

Xu-Dong Song(宋旭东), Shi-Hai Dong(董世海), Yu Zhang(张宇). Quantum information entropy for one-dimensional system undergoing quantum phase transition[J]. Chin. Phys. B, 2016, 25(5): 50302-050302.

参考文献 41

[1]	Yáñnez R J, van Assche W and Dehesa J S 1994 Phys. Rev. A 50 3065
[2]	van Assche W, Yáñnez R J and Dehesa J S 1995 J. Math. Phys. 36 4106
[3]	Aptekarev A L, Dehesa J S and Yáñnez R J 1994 J. Math. Phys. 35 4423
[4]	Sloane N J A and Wyner A D 1993 Shannon C E Collected Papers (New York: IEEE Press)
[5]	Everett H 1973 The Many World Interpretation of Quantum Mechannics
[6]	Hirschmann Jr I I 1957 Am. J. Math. 79 152
[7]	Beckner W 1975 Ann. Math. 102 159
[8]	Bialynicki-Birula I and Mycielski J 1975 Comm. Math. Phys. 44 129
[9]	Bialynicki-Birula I and Rudnicki 2010 arXiv: 1001.4668 [quant-ph]
[10]	Orlowski A 1997 Phys. Rev. A 56 2545
[11]	Atre R, Kumar A, Kumar C N and Panigrahi P 2004 Phys. Rev. A 69 052107
[12]	Romera E and de los Santos F 2007 Phys. Rev. Lett. 99 263601
[13]	Galindo A and Pascual P 1978 Quantum Mechanics (Berlin: Springer)
[14]	Angulo J C, Antolin J, Zarzo A and Cuchi J C 1999 Eur. Phys. J. D 7 479
[15]	Majernik V and Opatrný T 1996 J. Phys. A 29 2187
[16]	Dehesa J S, Martínez-Finkelshtein A and Sorokin V N 2006 Mol. Phys. 104 613.
[17]	Coffey M W 2007 Can. J. Phys. 85 733
[18]	Aydiner E, Orta C and Sever R 2008 Int. J. Mod. Phys. B 22 231
[19]	Dehesa J S, van Assche W and Yáñnez R J 1997 Methods Appl. Math. 4 91
[20]	Kumar A 2005 Ind J. Pure. Appl. Phys. 43 958
[21]	Dehesa J S, Yáñnez R J, Aptekarev A I and Buyarov V 1998 J. Math. Phys. 39 3050
[22]	Buyarov V S, Dehesa J S and Martinez-Finkelshtein A 1999 J. Approx. Theory 99 153
[23]	Buyarov V S, López-Artés P, Martínez-Finkelshtein A and van Assche W 2000 J. Phys. A 33 6549
[24]	Katriel J and Sen K D 2010 J. Comp. Appl. Math. 233 1399
[25]	Patil S H and Sen K D 2007 Int. J. Quant. Chem. 107 1864
[26]	Sen K D 2005 J. Chem. Phys. 123 074110
[27]	Sun G H and Dong S H 2013 Phys. Scr. 87 045003
[28]	Sun G H, Dong S H and Naad S 2013 Ann. Phys. 525 934
[29]	Sun G H, Avila Aoki M and Dong S H 2013 Chin. Phys. B 22 050302
[30]	Dong S, Sun G H, Dong S H and Draayer J P 2014 Phys. Lett. A 378 124
[31]	Yáñnez R-Navarro G, Sun G H, Dytrich T, Launey K D, Dong S H and Jerry J P 2014 Ann. Phys. 348 153
[32]	Valencia-Torres R, Sun G H and Dong S H 2015 Phys. Scr. 90 035205
[33]	Song X D, Sun G H and Dong S H 2015 Phys. Lett. A 379 1402
[34]	Falaye B J, Serrano F A and Dong S H 2016 Phys. Lett. A 380 267
[35]	Sun G H, Dusan P, Oscar C N and Dong S H 2015 Chin. Phys. B 24 100303
[36]	Iachello F and Zamfir N V 2004 Phys. Rev. Lett. 92 212501
[37]	Turner P S and Rowe D J 2005 Nucl. Phys. A 756 333
[38]	Iachello F and Levine R D 1995 Algebraic Theory of Molecules (Oxford, UK: Oxford University)
[39]	Zhang Y, Pan F, Liu Y X and Draayer J P 2010 J. Phys. B 43 225101
[40]	Zhao H X, Zhao H, Chen Y G and Yan Y H 2015 Acta Phys. Sin. 64 107101 (in Chinese)
[41]	Diao X F, Long C Y, Kong B and Long Z W 2015 Chin. Phys. Lett. 32 040301

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Quantum information entropy for one-dimensional system undergoing quantum phase transition

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 41

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model[J]. 中国物理B, 2022, 31(7): 70502-070502.
[2]	Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆). Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions[J]. 中国物理B, 2022, 31(6): 60505-060505.
[3]	Gaopei Pan(潘高培), Weilun Jiang(姜伟伦), and Zi Yang Meng(孟子杨). A sport and a pastime: Model design and computation in quantum many-body systems[J]. 中国物理B, 2022, 31(12): 127101-127101.
[4]	Hengcan Zhao(赵恒灿), Meng Lyu(吕孟), Jiahao Zhang(张佳浩), Shuai Zhang(张帅), and Peijie Sun(孙培杰). Quantum phase transitions in CePdAl probed by ultrasonic and thermoelectric measurements[J]. 中国物理B, 2022, 31(11): 117103-117103.
[5]	Yusong Cao(曹雨松), Junpeng Cao(曹俊鹏), and Heng Fan(范桁). Ferromagnetic Heisenberg spin chain in a resonator[J]. 中国物理B, 2021, 30(9): 90506-090506.
[6]	Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder[J]. 中国物理B, 2021, 30(8): 87501-087501.
[7]	Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets[J]. 中国物理B, 2021, 30(6): 67505-067505.
[8]	Hui-Fang Wang(王慧芳), Jin-Jun Zhang(张进军), and Jian-Jun Zhang(张建军). Classical-field description of Bose-Einstein condensation of parallel light in a nonlinear optical cavity[J]. 中国物理B, 2021, 30(11): 110301-110301.
[9]	赵博文, Jun Takahashi, Anders W. Sandvik. Tunable deconfined quantum criticality and interplay of different valence-bond solid phases[J]. 中国物理B, 2020, 29(5): 57506-057506.
[10]	陈臻, 邱岳寅, 张国强, 游建强. Dissipative quantum phase transition in a biased Tavis-Cummings model[J]. 中国物理B, 2020, 29(4): 44201-044201.
[11]	许雄, 方卯发. Reduction of entropy uncertainty for qutrit system under non-Markov noisy environment[J]. 中国物理B, 2020, 29(4): 40306-040306.
[12]	刘吉利, 梁九卿. Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime[J]. 中国物理B, 2019, 28(11): 110304-110304.
[13]	M Smidman, 沈斌, 郭春煜, 焦琳, 路欣, 袁辉球. Heavy fermions in high magnetic fields[J]. 中国物理B, 2019, 28(1): 17106-017106.
[14]	秦猛, 任中洲, 张欣. Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems[J]. 中国物理B, 2018, 27(6): 60301-060301.
[15]	张建军, 王慧芳, 候俊华. Enhanced second harmonic generation in a two-dimensional optical micro-cavity[J]. 中国物理B, 2018, 27(3): 34207-034207.