| GENERAL |
|
|
|
|
Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model |
| YUAN Zi-Gang1**, ZHANG Ping2 |
1School of Science, Beijing University of Chemical Technology, Beijing 100029
2Institute of Applied Physics and Computational Mathematics, Beijing 100088 |
|
| Cite this article: |
|
YUAN Zi-Gang, ZHANG Ping 2015 Chin. Phys. Lett. 32 060301 |
|
|
|
|
Abstract In our previous work [Phys. Rev. A 85 (2012) 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann–Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition (ESQPT) in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.
|
|
|
Received: 25 November 2014
Published: 30 June 2015
|
|
| PACS: |
03.65.Vf
|
(Phases: geometric; dynamic or topological)
|
| |
75.10.Pq
|
(Spin chain models)
|
| |
05.30.Pr
|
(Fractional statistics systems)
|
|
|
|
|
|
[1] Sachdev S 1999 Quantum Phase Transition (Cambridge: Cambridge University Press)
[2] Osterloh A, Amico L, Falci G and Fazio R 2002 Nature 416 608
[3] Vidal G, Latorre J I, Rico E and Kitaev A 2003 Phys. Rev. Lett. 90 227902
[4] Zanardi P and Paunkovi? N 2006 Phys. Rev. E 74 031123
[5] You W L, Li Y W and Gu S J 2007 Phys. Rev. E 76 022101
[6] Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Phys. Rev. Lett. 96 140604
[7] Sun Z, Wang X G and Sun C P 2007 Phys. Rev. A 75 062312
[8] Carollo A C M and Pachos J K 2005 Phys. Rev. Lett. 95 157203
[9] Zhu S L 2006 Phys. Rev. Lett. 96 077206
[10] Yuan Z G, Zhang P and Li S S 2007 Phys. Rev. A 75 012102
[11] Zhang A P and Li F L 2013 Chin. Phys. B 22 030308
[12] Dillenschneider R 2008 Phys. Rev. B 78 224413
[13] Sun Z, Lu X M and Song L J 2010 J. Phys. B: At. Mol. Opt. Phys. 43 215504
[14] Chen S, Wang L, Hao Y J and Wang Y P 2008 Phys. Rev. A 77 032111
[15] Campos Venuti L and Zanardi P 2007 Phys. Rev. Lett. 99 095701
[16] Pérez-Fernández P, Relaño A, Arias J M, Dukelsky J and García-Ramos J E 2009 Phys. Rev. A 80 032111
Relaño A, Arias J M, Dukelsky J, García-Ramos J E and Pérez-Fernández P 2008 Phys. Rev. A 78 060102
[17] Yuan Z G, Zhang P, Li S S, Jing J and Kong L B 2012 Phys. Rev. A 85 044102
[18] Cejnar P and Jolie J 2009 Prog. Part. Nucl. Phys. 62 210
[19] Vidal J, Arias J M, Dukelsky J and Garcia-Ramos J E 2006 Phys. Rev. C 73 054305
[20] Arias J M, Dukelsky J, Garcia-Ramos J E and Vidal J 2007 Phys. Rev. C 75 014301
[21] Fernandez F M 2004 Phys. Rev. B 69 037101
Balawender R, Holas A and March N H 2004 Phys. Rev. B 69 037103
Vatsya S R 2004 Phys. Rev. B 69 037102
Alon O E and Cederbaum L S 2003 Phys. Rev. B 68 033105
Zhang G P and George T F 2004 Phys. Rev. B 69 167102
[22] Barbar M N 1983 Phase Transition and Critical Phenomena (New York: Academic) p 145 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
