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Chin. Phys. B, 2016, Vol. 25(3): 030501    DOI: 10.1088/1674-1056/25/3/030501
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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      Published:  05 March 2016
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:  wcyu@phy.cuhk.edu.hk

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
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