Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(3): 030501    DOI: 10.1088/1674-1056/25/3/030501
GENERAL Prev   Next  

Fidelity spectrum: A tool to probe the property of a quantum phase

Wing Chi Yu, Shi-Jian Gu
Department of Physics and ITP, The Chinese University of Hong Kong, Hong Kong, China
Abstract  Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points, information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum. By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the two-dimensional Kitaev model on a honeycomb lattice. It was found that the spectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.
Keywords:  quantum phase transitions      quantum information      quantized spin models  
Received:  07 October 2015      Revised:  02 December 2015      Accepted manuscript online: 
PACS:  05.30.Rt (Quantum phase transitions)  
  64.70.Tg (Quantum phase transitions)  
  03.67.-a (Quantum information)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
Fund: Project supported by the Earmarked Research Grant from the Research Grants Council of HKSAR, China (Grant No. CUHK 401212).
Corresponding Authors:  Wing Chi Yu     E-mail:

Cite this article: 

Wing Chi Yu, Shi-Jian Gu Fidelity spectrum: A tool to probe the property of a quantum phase 2016 Chin. Phys. B 25 030501

[1] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)
[2] Carr L 2011 Understanding Quantum Phase Transitions (Boca Raton: CRC Press)
[3] Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Phys. Rev. Lett. 96 140604
[4] Zanardi P and Paunković 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] Zanardi P, Giorda P and Cozzini M 2007 Phys. Rev. Lett. 99 100603
[7] You W L and He L 2015 J. Phys.: Condens. Matter 27 205601
[8] Zhou H Q and Barjaktarevič J P 2008 J. Phys. A 41 412001
[9] Zhou H Q, Orŭs R and Vidal G 2008 Phys. Rev. Lett. 100 080601
[10] Gorin T, Prosen T, Seligman T H and žnidarič M 2006 Phys. Rep. 435 33
[11] Paunković N, Sacramento P, Nogueira P, Vieira V and Dugaev V 2008 Phys. Rev. A 77 052302
[12] Lu X M, Sun Z, Wang X and Zanardi P 2008 Phys. Rev. A 78 032309
[13] Wang X, Sun Z and Wang Z D 2009 Phys. Rev. A 79 012105
[14] Gu S J 2009 Chin. Phys. Lett. 26 026401
[15] Gu S J 2010 Int. J. Mod. Phys. B 24 4371
[16] Gu S J and Yu W C 2014 Europhys. Lett. 108 20002
[17] Venuti L C and Zanardi P 2007 Phys. Rev. Lett. 99 095701
[18] Gu S J, Kwok H M, Ning W Q and Lin H Q 2008 Phys. Rev. B 77 245109
[19] Albuquerque A F, Alet F, Sire C and Capponi S 2010 Phys. Rev. B 81 064418
[20] Rams M and Damski B 2011 Phys. Rev. Lett. 106 055701
[21] Gu S J, Yu W C and Lin H Q 2013 Int. J. Mod. Phys. B 27 1350106
[22] Sacramento P D, Paunković N and Vieira V R 2011 Phy. Rev. A 84 062318
[23] Wen X G 2004 Qunatum Field Theory of Many-body Systems (New York: Oxford University)
[24] Tasaki H 2000 arXiv:0009244[cond-mat]
[25] Kurchan J 2007 J. Stat. Mech. Theor. Exp. 2007 P07005
[26] Mukamel S 2003 Phys. Rev. Lett. 90 170604
[27] Pfeuty P 1970 Ann. Phys. 57 79
[28] Elliott R J, Pfeuty P and Wood C 1970 Phys. Rev. Lett. 25 443
[29] Jullien R, Pfeuty P, Fields J N and Doniach S 1978 Phys. Rev. B 18 3568
[30] Barouch E and McCoy B M 1970 Phys. Rev. A 2 1075
[31] Barouch E and McCoy B M 1971 Phys. Rev. A 3 786
[32] Coldea R, Tennant D, Wheeler E, Wawrzynska E, Prabhakaran D, Telling M, Habicht K, Smeibidl P and Kiefer K 2010 Science 327 177
[33] Damski B 2013 Phys. Rev. E 87 052131
[34] Deng S, Ortiz G and Viola L 2011 Phys. Rev. B 83 094304
[35] Rams M and Damski B 2011 Phys. Rev. A 84 032324
[36] Kitaev A 2006 Ann. Phys. (N.Y.) 443 312
[37] Chen H D and Nussinov Z 2008 J. Phys. A: Math. Theor. 41 075001
[38] Feng X Y, Zhang G M and Xiang T 2007 Phys. Rev. Lett. 98 087204
[39] Lee D H, Zhang G M and Xiang T 2007 Phys. Rev. Lett. 99 196805
[40] Baskaran G, Mandal S and Shankar R 2007 Phys. Rev. Lett. 98 247201
[41] Mondal S, Sen D and Sengupta K 2008 Phys. Rev. B 78 045101
[42] Shi X F, Yu Y, You J Q and Nori F 2009 Phys. Rev. B 79 134431
[43] Kitaev A 2003 Ann. Phys. 303 2
[44] Yang S, Gu S J, Sun C P and Lin H Q 2008 Phys. Rev. A 78 012304
[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] Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states
Xiao-Long Gong(龚小龙), Shuo Cao(曹硕), Yue Fang(方越), and Tong-Hua Liu(刘统华). Chin. Phys. B, 2022, 31(5): 050402.
[3] Quantum watermarking based on threshold segmentation using quantum informational entropy
Jia Luo(罗佳), Ri-Gui Zhou(周日贵), Wen-Wen Hu(胡文文), YaoChong Li(李尧翀), and Gao-Feng Luo(罗高峰). Chin. Phys. B, 2022, 31(4): 040302.
[4] Quantum storage of single photons with unknown arrival time and pulse shapes
Yu You(由玉), Gong-Wei Lin(林功伟), Ling-Juan Feng(封玲娟), Yue-Ping Niu(钮月萍), and Shang-Qing Gong(龚尚庆). Chin. Phys. B, 2021, 30(8): 084207.
[5] Improving the purity of heralded single-photon sources through spontaneous parametric down-conversion process
Jing Wang(王静), Chun-Hui Zhang(张春辉), Jing-Yang Liu(刘靖阳), Xue-Rui Qian(钱雪瑞), Jian Li(李剑), and Qin Wang(王琴). Chin. Phys. B, 2021, 30(7): 070304.
[6] 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.
[7] 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.
[8] Fast achievement of quantum state transfer and distributed quantum entanglement by dressed states
Liang Tian(田亮), Li-Li Sun(孙立莉), Xiao-Yu Zhu(朱小瑜), Xue-Ke Song(宋学科), Lei-Lei Yan(闫磊磊), Er-Jun Liang(梁二军), Shi-Lei Su(苏石磊), Mang Feng(冯芒). Chin. Phys. B, 2020, 29(5): 050306.
[9] Quantum fluctuation of entanglement for accelerated two-level detectors
Si-Xuan Zhang(张思轩), Tong-Hua Liu(刘统华), Shuo Cao(曹硕), Yu-Ting Liu(刘宇婷), Shuai-Bo Geng(耿率博), Yu-Jie Lian(连禹杰). Chin. Phys. B, 2020, 29(5): 050402.
[10] Error-detected single-photon quantum routing using a quantum dot and a double-sided microcavity system
A-Peng Liu(刘阿鹏), Liu-Yong Cheng(程留永), Qi Guo(郭奇), Shi-Lei Su(苏石磊), Hong-Fu Wang(王洪福), Shou Zhang(张寿). Chin. Phys. B, 2019, 28(2): 020301.
[11] A method to calculate effective Hamiltonians in quantum information
Jun-Hang Ren(任军航), Ming-Yong Ye(叶明勇), Xiu-Min Lin(林秀敏). Chin. Phys. B, 2019, 28(11): 110305.
[12] Effects of the Casimir force on the properties of a hybrid optomechanical system
Yi-Ping Wang(王一平), Zhu-Cheng Zhang(张筑城), Ya-Fei Yu(於亚飞), Zhi-Ming Zhang(张智明). Chin. Phys. B, 2019, 28(1): 014202.
[13] 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.
[14] 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.
[15] Quantum information processing with nitrogen-vacancy centers in diamond
Gang-Qin Liu(刘刚钦), Xin-Yu Pan(潘新宇). Chin. Phys. B, 2018, 27(2): 020304.
No Suggested Reading articles found!