Fidelity susceptibility and geometric phase in critical phenomenon

doi:10.1088/1674-1056/20/4/040302

Abstract Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC).

Keywords: fidelity susceptibility geometric phase quantum phase transition

Received: 05 November 2010
Revised: 10 December 2010
Accepted manuscript online:

PACS:	03.65.Fd	(Algebraic methods)
	03.67.-a	(Quantum information)
	03.65.Vf	(Phases: geometric; dynamic or topological)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11075101), the Shanghai Leading Academic Discipline Project, China (Grant No. S30105), and the Shanghai Research Foundation, China (Grant No. 07d222020).

Cite this article:

Tian Li-Jun(田立君), Zhu Chang-Qing(朱长青), Zhang Hong-Biao(张宏标), and Qin Li-Guo(秦立国) Fidelity susceptibility and geometric phase in critical phenomenon 2011 Chin. Phys. B 20 040302

[1]	Nielsen M and Chuang I 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp. 399--423
[2]	Zanardi P and Paunkovic N 2006 Phys. Rev. E 74 031123
[3]	Cozzini M, Giorda P and Zanardi P 2007 Phys. Rev. B 75 014439
[4]	Chen S, Wang L, Gu S J and Wang Y 2007 Phys. Rev. E 76 061108
[5]	Poht F M, Osenda O, Toloza J H and Serra P 2010 Phys. Rev. A 81 042518
[6]	Zanardi P, Quan H T, Wang X G and Sun C P 2007 Phys. Rev. A 75 032109
[7]	Buonsante P and Vezzani A 2007 Phys. Rev. Lett. 98 110601
[8]	Zanardi P, Giorda P and Cozzini M 2007 Phys. Rev. Lett. 99 100603
[9]	Wang Z, Ma T X, Gu S J and Lin H Q 2010 Phys. Rev. A 81 062350
[10]	Wang B, Feng M and Chen Z Q 2010 Phys. Rev. A 81 064301
[11]	Albuquerque A F, Alet F, Sire C and Capponi S 2010 Phys. Rev. B 81 064418
[12]	Gu S J 2009 Chin. Phys. Lett. 26 026401
[13]	Liu S M, He A Z and Ji Y J 2008 Chin. Phys. B 17 1248
[14]	Song W G and Tong P Q 2009 Chin. Phys. B 18 4707
[15]	Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) p. 3
[16]	Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Phys. Rev. Lett. 96 140604
[17]	You W L, Li Y W and Gu S J 2007 Phys. Rev E 76 022101
[18]	Zhang H B and Tian L J 2010 Chin. Phys. Lett. 27 050304
[19]	Carollo A C M and Pachos J K 2005 Phys. Rev. Lett. 95 157203
[20]	Zhu S L 2006 Phys. Rev. Lett. 96 077206
[21]	Cui H T, Li K and Yi X X 2006 Phys. Lett. A 360 243
[22]	Wang L C, Yan J Y and Yi X X 2010 Chin. Phys. B 19 040512
[23]	Pancharatnam S 1956 Proc. Ind. Acad. Sci. A 44 247
[24]	Berry M V 1984 Proc. Roy. Soc. A 392 45
[25]	Gu S J 2008 arXiv: 0811.3127v1 [quant-ph]
[26]	Lipkin H J, Meshkov N and Glick A J 1965 Nucl. Phys. 62 188
[27]	Lipkin H J, Meshkov N and Glick A J 1965 Nucl. Phys. 62 199
[28]	Lipkin H J, Meshkov N and Glick A J 1965 Nucl. Phys. 62 211
[29]	Cirac J I, Lewenstein M, Mupphilmer K and Zoller P 1998 Phys. Rev. A 57 1208
[30]	Josephson B D 1962 Phys. Lett. 1 251
[31]	Unanyan R G, Ionescu C and Fleischhauer M 2005 Phys. Rev. A 72 022326
[32]	Botet R and Jullien R 1983 Phys. Rev. B 28 3955
[33]	Holstein T and Primakoff H 1940 Phys. Rev. 58 1098
[34]	Dusuel S and Vidal J 2005 Phys. Rev. B 71 224420
[35]	Solomon A I, Feng Y and Penna V 1999 Phys. Rev. B 60 3044
[36]	Kwok H M, Ning W Q, Gu S J and Lin H Q 2008 Phys. Rev. E 78 032103 endfootnotesize

[1]	Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩). Chin. Phys. B, 2022, 31(7): 070502.
[2]	Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆). Chin. Phys. B, 2022, 31(6): 060505.
[3]	Geometric phase under the Unruh effect with intermediate statistics Jun Feng(冯俊), Jing-Jun Zhang(张精俊), and Qianyi Zhang(张倩怡). Chin. Phys. B, 2022, 31(5): 050312.
[4]	A sport and a pastime: Model design and computation in quantum many-body systems Gaopei Pan(潘高培), Weilun Jiang(姜伟伦), and Zi Yang Meng(孟子杨). Chin. Phys. B, 2022, 31(12): 127101.
[5]	Quantum phase transitions in CePdAl probed by ultrasonic and thermoelectric measurements Hengcan Zhao(赵恒灿), Meng Lyu(吕孟), Jiahao Zhang(张佳浩), Shuai Zhang(张帅), and Peijie Sun(孙培杰). Chin. Phys. B, 2022, 31(11): 117103.
[6]	Ferromagnetic Heisenberg spin chain in a resonator Yusong Cao(曹雨松), Junpeng Cao(曹俊鹏), and Heng Fan(范桁). Chin. Phys. B, 2021, 30(9): 090506.
[7]	Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[8]	Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets 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). Chin. Phys. B, 2021, 30(6): 067505.
[9]	Quantum simulations with nuclear magnetic resonance system Chudan Qiu(邱楚丹), Xinfang Nie(聂新芳), and Dawei Lu(鲁大为). Chin. Phys. B, 2021, 30(4): 048201.
[10]	Equilibrium dynamics of the sub-ohmic spin-boson model at finite temperature Ke Yang(杨珂) and Ning-Hua Tong(同宁华). Chin. Phys. B, 2021, 30(4): 040501.
[11]	Classical-field description of Bose-Einstein condensation of parallel light in a nonlinear optical cavity Hui-Fang Wang(王慧芳), Jin-Jun Zhang(张进军), and Jian-Jun Zhang(张建军). Chin. Phys. B, 2021, 30(11): 110301.
[12]	Geometry of time-dependent $\mathcal{PT}$-symmetric quantum mechanics Da-Jian Zhang(张大剑), Qing-hai Wang(王清海), and Jiangbin Gong(龚江滨). Chin. Phys. B, 2021, 30(10): 100307.
[13]	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.
[14]	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.
[15]	Geometric phase of an open double-quantum-dot system detected by a quantum point contact Qian Du(杜倩), Kang Lan(蓝康), Yan-Hui Zhang(张延惠), Lu-Jing Jiang(姜露静). Chin. Phys. B, 2020, 29(3): 030302.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Fidelity susceptibility and geometric phase in critical phenomenon

Cite this article:

Online attention