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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.
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Keywords:
- quantum phase transition /
- MERA /
- reduced density matrix /
- fidelity
[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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[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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