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We use the multi-scale entanglement reorganization ansatz algorithm to simulate the spin 1/2 quantum XYX model and determine its ground-state phase diagram and entanglement phase diagram by using local order parameter and characterizing quantum entanglement: one-tangle, concurrence, and entanglement ratio R. We find that the information in entanglement phase diagram is more than in ground-state phase diagram. In addition, we extract the critical exponents β and ν from the numerical data near critical point.
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Keywords:
- quantum entanglement /
- multi-scale entanglement reorganization ansatz /
- quantum phase transitions /
- critical exponent
[1] Syljuasen O F 2003 Phys. Rev. A 68 060301(R)
[2] Schrödinger E 1935 Proc. Cambridge Philos. Soc. 31 555
[3] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[4] Amico L, Osterloh A, Plastina F, Fazio R, Massimo P G 2004 Phys. Rev. A 69 022304
[5] Roscilde T, Verrucchi P, Fubini A, Haas S, Tognetti V 2004 Phys. Rev. Lett. 93 167203
[6] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
[7] Gu S J, Lin H Q, Li Y Q 2003 Phys. Rev. A 68 042330
[8] Chung Y H, Landau D P 2011 Phys. Rev. B 83 113104
[9] Kopp A, Jia X, Chakravarty S 2006 Ann. Phys. 322 1466
[10] Chen Y, Zanardi P, Wang Z D, Zhang F C 2006 New J. Phys. 8 97
[11] Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517
[12] Si L M, Hou J X 2008 Science China G 38 1558 (in Chinese) [司黎明, 侯吉旋 2008 中国科学G辑 38 1558]
[13] Wang F, Jia H H, Zhang H L, Zhang X A, Chang S L 2009 Science China G 39 1052 (in Chinese) [王飞, 贾红辉, 张海良, 张学骜, 常胜利 2009 中国科学G辑 39 1052]
[14] 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]
[15] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) p3
[16] Vidal G 2007 Phys. Rev. Lett. 99 220405
[17] Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[18] Vidal G 2007 Phys. Rev. Lett. 98 070201
[19] Jordan J, Orus R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[20] Yang C N , Yang C P 1966 Phys. Rev. B 150 321
[21] Dmitriev D V, Krivnov V Y, Ovchinnikov A A 2002 Phys. Rev. B 65 172409
[22] Kurmann J, Thomas H, Muller G 1982 Physica 112A 235
[23] Evenbly G, Vidal G 2011 arXiv: 1109.5334 [cond-mat]
[24] Amico L, Osterloh A 2004 Phys. Rev. A 69 022304
[25] Zhao J H, Wang H L, Li B, Zhou H Q 2010 Phys. Rev. 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] Dmitriev D V, Krivnov V Ya, Ovchinnikov A A, Langari A 2002 J. Exp. Theor. Phys. 95 538
[28] Tagliacozzo L, de Oliveira Thiago R, Iblisdir S, Latorre J I 2008 Phys. Rev. B 78 024410
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[1] Syljuasen O F 2003 Phys. Rev. A 68 060301(R)
[2] Schrödinger E 1935 Proc. Cambridge Philos. Soc. 31 555
[3] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[4] Amico L, Osterloh A, Plastina F, Fazio R, Massimo P G 2004 Phys. Rev. A 69 022304
[5] Roscilde T, Verrucchi P, Fubini A, Haas S, Tognetti V 2004 Phys. Rev. Lett. 93 167203
[6] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
[7] Gu S J, Lin H Q, Li Y Q 2003 Phys. Rev. A 68 042330
[8] Chung Y H, Landau D P 2011 Phys. Rev. B 83 113104
[9] Kopp A, Jia X, Chakravarty S 2006 Ann. Phys. 322 1466
[10] Chen Y, Zanardi P, Wang Z D, Zhang F C 2006 New J. Phys. 8 97
[11] Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517
[12] Si L M, Hou J X 2008 Science China G 38 1558 (in Chinese) [司黎明, 侯吉旋 2008 中国科学G辑 38 1558]
[13] Wang F, Jia H H, Zhang H L, Zhang X A, Chang S L 2009 Science China G 39 1052 (in Chinese) [王飞, 贾红辉, 张海良, 张学骜, 常胜利 2009 中国科学G辑 39 1052]
[14] 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]
[15] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press) p3
[16] Vidal G 2007 Phys. Rev. Lett. 99 220405
[17] Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[18] Vidal G 2007 Phys. Rev. Lett. 98 070201
[19] Jordan J, Orus R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[20] Yang C N , Yang C P 1966 Phys. Rev. B 150 321
[21] Dmitriev D V, Krivnov V Y, Ovchinnikov A A 2002 Phys. Rev. B 65 172409
[22] Kurmann J, Thomas H, Muller G 1982 Physica 112A 235
[23] Evenbly G, Vidal G 2011 arXiv: 1109.5334 [cond-mat]
[24] Amico L, Osterloh A 2004 Phys. Rev. A 69 022304
[25] Zhao J H, Wang H L, Li B, Zhou H Q 2010 Phys. Rev. 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] Dmitriev D V, Krivnov V Ya, Ovchinnikov A A, Langari A 2002 J. Exp. Theor. Phys. 95 538
[28] Tagliacozzo L, de Oliveira Thiago R, Iblisdir S, Latorre J I 2008 Phys. Rev. B 78 024410
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