Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(5): 050302    DOI: 10.1088/1674-1056/25/5/050302
GENERAL Prev   Next  

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
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 Sx and the momentum entropy Sp 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.
Keywords:  quantum information entropy      quantum phase transition      entropy uncertainty relation     
Received:  16 December 2015      Published:  05 May 2016
PACS:  03.65.-w (Quantum mechanics)  
  03.65.Ge (Solutions of wave equations: bound states)  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.
Corresponding Authors:  Yu Zhang     E-mail:

Cite this article: 

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 2016 Chin. Phys. B 25 050302

[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
[1] Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[2] Dissipative quantum phase transition in a biased Tavis-Cummings model
Zhen Chen(陈臻), Yueyin Qiu(邱岳寅), Guo-Qiang Zhang(张国强), Jian-Qiang You(游建强). Chin. Phys. B, 2020, 29(4): 044201.
[3] Reduction of entropy uncertainty for qutrit system under non-Markov noisy environment
Xiong Xu(许雄), Mao-Fa Fang(方卯发). Chin. Phys. B, 2020, 29(4): 040306.
[4] Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime
Ji-Li Liu(刘吉利), Jiu-Qing Liang(梁九卿). Chin. Phys. B, 2019, 28(11): 110304.
[5] Heavy fermions in high magnetic fields
M Smidman, B Shen(沈斌), C Y Guo(郭春煜), L Jiao(焦琳), X Lu(路欣), H Q Yuan(袁辉球). Chin. Phys. B, 2019, 28(1): 017106.
[6] Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems
Meng Qin(秦猛), Zhongzhou Ren(任中洲), Xin Zhang(张欣). Chin. Phys. B, 2018, 27(6): 060301.
[7] Enhanced second harmonic generation in a two-dimensional optical micro-cavity
Jian-Jun Zhang(张建军), Hui-Fang Wang(王慧芳), Jun-Hua Hou(候俊华). Chin. Phys. B, 2018, 27(3): 034207.
[8] Phase diagram characterized by transmission in a triangular quantum dot
Jin Huang(黄金), Wei-Zhong Wang(王为忠). Chin. Phys. B, 2018, 27(11): 117303.
[9] Phase transition and charge transport through a triple dot device beyond the Kondo regime
Yong-Chen Xiong(熊永臣), Zhan-Wu Zhu(朱占武), Ze-Dong He(贺泽东). Chin. Phys. B, 2018, 27(10): 108503.
[10] Equilibrium dynamics of the sub-Ohmic spin-boson model under bias
Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华). Chin. Phys. B, 2017, 26(6): 060501.
[11] Dynamical correlation functions of the quadratic coupling spin-Boson model
Da-Chuan Zheng(郑大川), Ning-Hua Tong(同宁华). Chin. Phys. B, 2017, 26(6): 060502.
[12] Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures
Majeed Ur Rehman, A A Abid. Chin. Phys. B, 2017, 26(12): 127304.
[13] Quantum oscillations and nontrivial transport in (Bi0.92In0.08)2Se3
Minhao Zhang(张敏昊), Yan Li(李焱), Fengqi Song(宋凤麒), Xuefeng Wang(王学锋), Rong Zhang(张荣). Chin. Phys. B, 2017, 26(12): 127305.
[14] Quantum correlations dynamics of three-qubit states coupled to an XY spin chain:Role of coupling strengths
Shao-Ying Yin(尹少英), Qing-Xin Liu(刘庆欣), Jie Song(宋杰), Xue-Xin Xu(许学新), Ke-Ya Zhou(周可雅), Shu-Tian Liu(刘树田). Chin. Phys. B, 2017, 26(10): 100501.
[15] Fidelity spectrum: A tool to probe the property of a quantum phase
Wing Chi Yu, Shi-Jian Gu. Chin. Phys. B, 2016, 25(3): 030501.
No Suggested Reading articles found!