Symmetry-breaking effects upon bipartite and multipartite entanglement in the XY model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 3, 2008, Pages

  De Oliveira, Thiago R ^a   Rigolin, Gustavo ^a   De Oliveira, Marcos C ^a   Miranda, E ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL SYMMETRY; ELECTRON CORRELATIONS; FERROMAGNETISM; GROUND STATE; MAGNETIC FIELD EFFECTS; MATHEMATICAL MODELS; ONE DIMENSIONAL; PHASE TRANSITIONS;

QUANTUM CRITICAL POINTS; QUANTUM PHASE TRANSITIONS; SYMMETRY BREAKING;

QUANTUM ENTANGLEMENT;

EID: 40949149008     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.032325     Document Type: Article

References (60)

1. P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin/Cummings, Menlo Park, 1984).
2. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001).
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
4. P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042101 65, 042101 (2002)
5. P. Zanardi and X. Wang, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/ 37/307 35, 7947 (2002).
6. T. J. Osborne and M. A. Nielsen, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1019601218492 1, 45 (2002).
7. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
8. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
9. L.-A. Wu, M. S. Sarandy, and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.250404 93, 250404 (2004).
10. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
11. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
12. L. Campos Venuti, C. Degli Esposti Boschi, M. Roncaglia, and A. Scaramucci, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.010303 73, 010303 (R) (2006).
13. L.-A. Wu, M. S. Sarandy, D. A. Lidar, and L. J. Sham, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.052335 74, 052335 (2006).
14. M.-F. Yang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.030302 71, 030302 (R) (2005).
15. J. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062318 73, 062318 (2006).
16. S.-J. Gu, G.-S. Tian, and H.-Q. Lin, N. J. Phys. 8, 61 (2006). 1367-2630
17. D. Larsson and H. Johannesson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.042320 73, 042320 (2006).
18. X. Wang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.012313 64, 012313 (2001).
19. J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 10.1103/PhysRevLett.90.227902 4, 48 (2004).
20. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003).
21. C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1994).
22. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2004), P06002.
23. A. R. Its, B.-Q. Jin, and V. E. Korepin, J. Phys. A JPHAC5 0305-4470 38, 2975 (2005)
24. A. R. Its, B.-Q. Jin, and V. E. Korepin, e-print arXiv:quant-ph/0606178v3
25. F. Franchini, A. R. Its, B.-Q. Jin, and V. E. Korepin, e-print arXiv:quant-ph/0606240v1.
26. T.-C. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.060305 71, 060305 (R) (2005).
27. L. Amico, F. Baroni, A. Fubini, D. Patanè, V. Tognetti, and P. Verrucchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022322 74, 022322 (2006).
28. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000).
29. P. Stelmachovic and V. Buzek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.032313 70, 032313 (2004).
30. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.027901 92, 027901 (2004)
31. M. Popp, F. Verstraete, M. A. Martín-Delgado, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042306 71, 042306 (2005).
32. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087201 92, 087201 (2004).
33. G. Gour and R. W. Spekkens, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062331 73, 062331 (2006).
34. P. Zanardi and N. Paunković, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.031123 74, 031123 (2006)
35. P. Zanardi, P. Giorda, and M. Cozzini, e-print arXiv:quant-ph/0701061v1.
36. L. Amico, A. Osterloh, F. Plastina, R. Fazio, and G. M. Palma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022304 69, 022304 (2004).
37. T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, and V. Tognetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.167203 93, 167203 (2004)
38. A. Anfossi, P. Giorda, A. Montorsi, and F. Traversa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.207206 95, 207206 (2005).
39. H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203 93, 227203 (2004).
40. Y. Chen, P. Zanardi, Z. D. Wang, and F. C. Zhang, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/6/097 8, 97 (2006).
41. Y. Chen, Z. D. Wang, and F. C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.224414 73, 224414 (2006).
42. J. I. Latorre, C. A. Lütken, E. Rico, and G. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.034301 71, 034301 (2005).
43. P. Pfeuty, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(70)90270- 8 57, 79 (1970).
44. E. Barouch, B. M. McCoy, and M. Dresden, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.2.1075 2, 1075 (1970).
45. E. Barouch and B. M. McCoy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.3.786 3, 786 (1971).
46. J. D. Johnson and B. M. McCoy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.4.2314 4, 2314 (1971).
47. T. R. de Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.010305 73, 010305 (R) (2006).
48. G. Rigolin, T. R. de Oliveira, and M. C. de Oliveira, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022314 74, 022314 (2006).
49. D. A. Meyer and N. R. Wallach, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1497700 43, 4273 (2002).
50. T. R. de Oliveira, G. Rigolin, M. C. de Oliveira, and E. Miranda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.170401 97, 170401 (2006).
51. The literature on entanglement in quantum phase transitions is already too extensive to be fully listed in this Introduction. We simply outline key papers related to the main subjects discussed in our developments. For a recent review on entanglement in many-body system see L. Amico, R. Fazio, A. Osterloh, and V. Vedral, e-print arXiv:quant-ph/0703044v1.
52. G. K. Brennen, Quantum Inf. Comput. QICUAW 1533-7146 3, 619 (2003).
53. A. J. Scott, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052330 69, 052330 (2004).
54. For perhaps the earliest discussion of why and how this comes about, see P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.86.694 86, 694 (1952).
55. P. A. Vieira (private communication).
56. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
57. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
58. O. F. Syljuåsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68. 060301 68, 060301 (R) (2003).
59. A. Osterloh, G. Palacios, and S. Montangero, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.257201 97, 257201 (2006).
60. F. Baroni, A. Fubini, V. Tognetti, and P. Verrucchi, J. Phys. A JPHAC5 0305-4470 10.1088/1751-8113/40/32/010 40, 9845 (2007).