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Ground state phase diagram of the quantum spin 1 Blume-Capel model: reduced density fidelity study

Zhao Jian-Hui

Ground state phase diagram of the quantum spin 1 Blume-Capel model: reduced density fidelity study

Zhao Jian-Hui
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  • The reduced density fidelity is a measure of distance between two reduced density matrix, which can be used to characterize quantum phase transitions in quantum many-body systems. In this paper, we use the multi-scale entanglement reorganization ansatz (MERA) algorithm to simulate the spin 1 quantum Blume-Capel model and determine its ground-state phase diagram through calculating the reduced density fidelity. The qualitative relevant information contained in one site reduced density matrix is different from that contained two-site reduced density matrix, which can be detected by using the reduced density fidelity. In addition, we also characterize quantum phase transitions in quantum many-body systems by using the local parameters and energy gaps.
    • Funds: Project supported by the Chongqing Postdoctoral Sustentation Fund (Grant No. CQXM201103019).
    [1]

    Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) p3

    [2]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [3]

    Amico L, Andreas Osterloh, Francesco Plastina, Rosario Fazio, Massimo Palma G 2004 Phys. Rev. A 69 022304

    [4]

    Tommaso Roscilde, Paola Verrucchi, Andrea Fubini, Stephan Haas, Valerio Tognetti 2004 Phys. Rev. Lett. 93 167203

    [5]

    Valerie Coffman, Joydip Kundu, Wootters W K 2000 Phys. Rev. A 61, 052306

    [6]

    Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267 (in Chinese) [蔡卓, 陆文彬, 刘拥军 2008 物理学报 57 7267]

    [7]

    Vidal G 2007 Phys. Rev. Lett. 98 070201

    [8]

    Jordan J, Orus R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602

    [9]

    Li B, Li S H, Zhou H Q 2009 Phys. Rev. B 79 060101(R)

    [10]

    Vidal G 2007 Phys. Rev. Lett. 99 220405

    [11]

    Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108

    [12]

    Glen Evenbly, Guifre Vidal 2011 arXiv:1109.5334

    [13]

    Nightingale M P 1976 Physica A 83 561

    [14]

    Hu B, 1980 Phys. Rev. Lett. 75 A 372

    [15]

    Blume M, Emery V J, Griffiths R B 1971 Phys. Rev. A 4 1071

    [16]

    Alcaraz F C, Drugowich de Felicio J R, Stilck J F 1985 Phys. Rev. B 32 7469

    [17]

    Griffiths R B 1970 Phys. Rev. Lett. 24 715

    [18]

    Peliti L, Leiblen S 1984 Phys. Rev. B 29 1253

    [19]

    Hamber H 1980 Phys. Rev. B 21 3999

    [20]

    Blume M 1966 Phys. Rev. 141 517

    [21]

    Capel H W 1967 Physica 37 423

    [22]

    Zhou H Q, Barjaktarevic J P 2008 J. Phys. A: Math. Theor. 41 412001

    [23]

    Zhou H Q, Roman Orus, Guifre Vidal 2008 Physical Review Letters 100 080601

    [24]

    Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge University Press, Cambrige) p409

    [25]

    Zhao J H, Wang H L, Li B, Zhou H Q 2010 Physical Review E 82 061127

    [26]

    Liu J H, Shi Q Q, Zhao J H, Zhou H Q 2011 J. Phys. A: Math. Theor. 44 495302

    [27]

    Arizmendi C M, Epele L N, Fanchiotti, Garcia Canal C A 1986 Z. Phys. B Condensed Matter 64 231 235

    [28]

    Xavier J C, Alcaraz F C 2011 Phys. Rev. B 84 094410

    [29]

    Feng D, Jin G J 2003 Condensed Matter Physics (Vol. 1) (Beijing: Higher Education Press) p601 (in Chinese) [冯端, 金国钧 2003 凝聚态物理学 (上卷) (北京: 高等教育出版社) 第601页]

  • [1]

    Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) p3

    [2]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [3]

    Amico L, Andreas Osterloh, Francesco Plastina, Rosario Fazio, Massimo Palma G 2004 Phys. Rev. A 69 022304

    [4]

    Tommaso Roscilde, Paola Verrucchi, Andrea Fubini, Stephan Haas, Valerio Tognetti 2004 Phys. Rev. Lett. 93 167203

    [5]

    Valerie Coffman, Joydip Kundu, Wootters W K 2000 Phys. Rev. A 61, 052306

    [6]

    Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267 (in Chinese) [蔡卓, 陆文彬, 刘拥军 2008 物理学报 57 7267]

    [7]

    Vidal G 2007 Phys. Rev. Lett. 98 070201

    [8]

    Jordan J, Orus R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602

    [9]

    Li B, Li S H, Zhou H Q 2009 Phys. Rev. B 79 060101(R)

    [10]

    Vidal G 2007 Phys. Rev. Lett. 99 220405

    [11]

    Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108

    [12]

    Glen Evenbly, Guifre Vidal 2011 arXiv:1109.5334

    [13]

    Nightingale M P 1976 Physica A 83 561

    [14]

    Hu B, 1980 Phys. Rev. Lett. 75 A 372

    [15]

    Blume M, Emery V J, Griffiths R B 1971 Phys. Rev. A 4 1071

    [16]

    Alcaraz F C, Drugowich de Felicio J R, Stilck J F 1985 Phys. Rev. B 32 7469

    [17]

    Griffiths R B 1970 Phys. Rev. Lett. 24 715

    [18]

    Peliti L, Leiblen S 1984 Phys. Rev. B 29 1253

    [19]

    Hamber H 1980 Phys. Rev. B 21 3999

    [20]

    Blume M 1966 Phys. Rev. 141 517

    [21]

    Capel H W 1967 Physica 37 423

    [22]

    Zhou H Q, Barjaktarevic J P 2008 J. Phys. A: Math. Theor. 41 412001

    [23]

    Zhou H Q, Roman Orus, Guifre Vidal 2008 Physical Review Letters 100 080601

    [24]

    Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge University Press, Cambrige) p409

    [25]

    Zhao J H, Wang H L, Li B, Zhou H Q 2010 Physical Review E 82 061127

    [26]

    Liu J H, Shi Q Q, Zhao J H, Zhou H Q 2011 J. Phys. A: Math. Theor. 44 495302

    [27]

    Arizmendi C M, Epele L N, Fanchiotti, Garcia Canal C A 1986 Z. Phys. B Condensed Matter 64 231 235

    [28]

    Xavier J C, Alcaraz F C 2011 Phys. Rev. B 84 094410

    [29]

    Feng D, Jin G J 2003 Condensed Matter Physics (Vol. 1) (Beijing: Higher Education Press) p601 (in Chinese) [冯端, 金国钧 2003 凝聚态物理学 (上卷) (北京: 高等教育出版社) 第601页]

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    [7] Zhao Jian-Hui, Wang Hai-Tao. Quantum phase transition and ground state entanglement of the quantum spin system: a MERA study. Acta Physica Sinica, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
    [8] Lü Jing-Fen, Ma Shan-Jun. Fidelity of the photon subtracted (or added) squeezed vacuum state and squeezed cat state. Acta Physica Sinica, 2011, 60(8): 080301. doi: 10.7498/aps.60.080301
    [9] Qin Meng, Li Yan-Biao, Bai Zhong, Wang Xiao. Effects of different Dzyaloshinskii-Moriya interaction and magnetic field on entanglement and fidelity intrinsic decoherence in a spin system. Acta Physica Sinica, 2014, 63(11): 110302. doi: 10.7498/aps.63.110302
    [10] Ren Jie, Gu Li-Ping, You Wen-Long. Fidelity susceptibility and entanglement entropy in S=1 quantum spin chain with three-site interactions. Acta Physica Sinica, 2018, 67(2): 020302. doi: 10.7498/aps.67.20172087
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  • Received Date:  30 March 2012
  • Accepted Date:  26 May 2012
  • Published Online:  20 November 2012

Ground state phase diagram of the quantum spin 1 Blume-Capel model: reduced density fidelity study

  • 1. Postdoctoral Research Station of Materials Science and Engineering, Chongqing University, Chongqing 400030, China
Fund Project:  Project supported by the Chongqing Postdoctoral Sustentation Fund (Grant No. CQXM201103019).

Abstract: The reduced density fidelity is a measure of distance between two reduced density matrix, which can be used to characterize quantum phase transitions in quantum many-body systems. In this paper, we use the multi-scale entanglement reorganization ansatz (MERA) algorithm to simulate the spin 1 quantum Blume-Capel model and determine its ground-state phase diagram through calculating the reduced density fidelity. The qualitative relevant information contained in one site reduced density matrix is different from that contained two-site reduced density matrix, which can be detected by using the reduced density fidelity. In addition, we also characterize quantum phase transitions in quantum many-body systems by using the local parameters and energy gaps.

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