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

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

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.

Keywords: quantum information entropy quantum phase transition entropy uncertainty relation

Received: 16 December 2015
Revised: 11 January 2016
Accepted manuscript online:

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: dlzhangyu_physics@163.com

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

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