Bipartite entanglement and entropic boundary law in lattice spin systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 2, 2005, Pages

  Hamma, Alioscia ^a,b   Ionicioiu, Radu ^a   Zanardi, Paolo ^a  

^a ISI FOUNDATION   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; GROUND STATE; MATHEMATICAL MODELS; POLARIZATION; SURFACES;

BIPARTITE ENTANGLEMENT; KITAEV'S MODEL; PERIMETER; SQUARE LATTICE;

ENTROPY;

EID: 33344464491     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.022315     Document Type: Article

References (40)

1. For reviews, see D. P. DiVincenzo and C. Bennett, Nature (London) NATUAS 0028-0836 10.1038/35005001 404, 247 (2000);
2. A. Steane, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/61/2/002 61, 117 (1998).
3. P. Zanardi and X. Wang, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/ 37/307 35, 7947 (2002).
4. A. Botero and B. Reznik, e-print quant-ph 0404176.
5. X. G. Wen, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00808-3 300, 175 (2002).
6. T. J. Osborne and M. A. Nielsen Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevLett.80.869 66, 32110 (2002);
7. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002);
8. J. Vidal, G. Palacios, and R. Mosseri, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.22107 69, 22107 (2004).
9. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.147902 91, 147902 (2003).
10. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003);
11. J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 10.1103/PhysRevLett.90.227902 4, 48 (2004).
12. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.27901 92, 27901 (2004);
13. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087201 92, 087201 (2004).
14. A. R. Its, B. Q. Jin, and V. E. Korepin, e-print quant-ph 0409027.
15. H. Li, X. Wang, and Y. Li, e-print quant-ph 0403178.
16. A. Hamma, R. Ionicioiu, and P. Zanardi, e-print quant-ph 0406202.
17. M. H. Freedman, A. Kitaev, and Z. Wang, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s002200200635 227, 587 (2002);
18. M. Freedman, M. Larsen, and Z. Wang, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s002200200645 227, 605 (2002);
19. M. H. Freedman, Found Comput. Math. 1615-3375 1, 183 (2001);
20. M. H. Freedman, A. Kitaev, M. J. Larsen, and Z. Wang, Bull., New Ser., Am. Math. Soc. 0273-0979 10.1090/S0273-0979-02-00964-3 40, 31 (2003).
21. A. Y. Kitaev, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/S0003-4916(02) 00018-0 303, 2 (2003).
22. X. G. Wen and Q. Niu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.41. 9377 41, 9377 (1990);
23. X. G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 016803 90, 016803 (2003);
24. X. G. Wen and A. Zee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58. 15717 58, 15717 (1998);
25. X. G. Wen, Adv. Phys. ADPHAH 0001-8732 44, 405 (1995).
26. G. 't Hooft, e-print gr-qc 9310026;
27. L. Susskind, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.531249 36, 6377 (1995);
28. R. Bousso, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.825 74, 825 (2002).
29. D. Fattal, T. S. Cubitt, Y. Yamamoto, S. Bravyi, and I. L. Chuang, e-print quant-ph 0406168.
30. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.1559 48, 1559 (1982).
31. V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 20, 1064 (1950).
32. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
33. C. Callan and F. Wilczek, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(94)91007-3 333, 55 (1994);
34. G. 't Hooft, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(85)90418-3 256, 727 (1985).
35. C. Holzney, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1994).
36. T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.50.3987 50, 3987 (1994).
37. J. D. Beckenstein, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.7.2333 7, 2333 (1973);
38. S. W. Hawking, Commun. Math. Phys. CMPHAY 0010-3616 43, 199 (1975).
39. M. Srednicki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71. 666 71, 666 (1993).
40. M. B. Plenio, J. Eisert, J. Dreißig, and M. Cramer, e-print quant-ph 0405142.