2D multipartite valence bond states in quantum anti-ferromagnets

Annals of Physics

Volumn 323, Issue 9, 2008, Pages 2115-2131

  Rico, E ^a,b,c   Briegel, H J ^a,b  

^a UNIVERSITY OF INNSBRUCK   (Austria)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c UNIVERSITY OF VIENNA   (Austria)

Author keywords

Mott Hubbard insulator; Quantum anti ferromagnet; Valence bond state

Indexed keywords

EID: 48749120051     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2008.03.006     Document Type: Article

References (74)

1. Bardeen J., Cooper L.N., and Schrieffer J.R. Phys. Rev. 108 (1957) 1175-1204
2. Laughlin R.B. Phys. Rev. Lett. 50 (1983) 1395
3. Fradkin E. Field Theories of Condensed Matter systems (1991), Addison-Wesley
4. Auerbach A. Interacting Electrons and Quantum Magnetism (1994), Springer
5. Essler F.H.L., Frahm H., Goehmann F., Kluemper A., and Korepin V.E. The One-Dimensional Hubbard Model (2005), Cambridge University Press
6. Rokhsar D.S., and Kivelson S.A. Phys. Rev. Lett. 61 (1988) 2376
7. Moessner R., and Sondhi S.L. Phys. Rev. Lett. 86 (2001) 1881
8. Misguich G., and Lhuillier C. Frustrated Spin Systems (2005), World Scientific
9. Anderson P.W. Science 235 (1987) 1196
10. Zhang F.C., and Rice T.M. Phys. Rev. B37 (1988) 3759
11. Ramirez A.P. J. Phys. Condens. Matter 9 (1997) 8171
12. Bennett C.H., and DiVincenzo D.P. Nature 404 (2000) 247
13. Nielsen M.A., and Chuang I.L. Quantum Computation and Quantum Information (2000), Cambridge University Press
14. Entanglement: theory and experiment, Qunat. Inf. Comp., 1, 2001 (special issue).
15. D. Estève, J.M. Raimond, J. Dalibard, (eds.), Quantum Entanglement and Information Processing, Les Houches, Session LXXIX, 2003.
16. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys., quant-ph/0703044, 2007.
17. Preskill J. J. Mod. Opt. 47 (2000) 127-137
18. Wen X.G. Phys. Lett. A300 (2002) 175
19. D. Gottesman, Stabilizer Codes and Quantum Error Correction, Ph.D. Thesis, Caltech, 1997.
20. Raussendorf R., and Briegel H.J. Phys. Rev. Lett. 86 (2001) 5188
21. Levin M.A., and Wen X.G. Phys. Rev. B71 (2005) 045110
22. Kitaev A. Ann. Phys. 321 (2006) 2
23. Bombin H., and Martin-Delgado M.A. Phys. Rev. Lett. 97 (2006) 180501
24. Kitaev A. Ann. Phys. 303 (2003) 2
25. Freedman M.H., Kitaev A., Larsen M.J., and Wang Z. Bull. Am. Math. Soc. 40 (2002) 31
26. Affleck I., Kennedy T., Lieb E.H., and Tasaki H. Phys. Rev. Lett. 59 (1987) 799
27. Affleck I., Kennedy T., Lieb E.H., and Tasaki H. Commun. Math. Phys. (1988) 477
28. Haldane F.D.M. Phys. Lett. A93 (1983) 464
29. Haldane F.D.M. Phys. Rev. Lett. 50 (1983) 1153
30. Girvin S.M., and Arovas D.P. Phys. Scripta T(27) (1989) 156
31. den Nijs M., and Rommelse K. Phys. Rev. B40 (1989) 4709
32. Verstraete F., Popp M., and Cirac J.I. Phys. Rev. Lett. 92 (2004) 027901
33. Verstraete F., Martin-Delgado M.A., and Cirac J.I. Phys. Rev. Lett. 92 (2004) 087201
34. Popp M., Verstraete F., Martin-Delgado M.A., and Cirac J.I. Phys. Rev. A71 (2005) 042306
35. Kluemper A., Schadschneider A., and Zittartz J. Europhys. Lett. 24 (1993) 293
36. Ostlund S., and Rommer S. Phys. Rev. Lett. 75 (1995) 3537
37. Fan H., Korepin V., and Roychowdhury V. Phys. Rev. Lett. 93 22 (2004) 227203
38. Gomez C., Ruiz-Altaba M., and Sierra G. Quantum Groups in Two-Dimensional Physics (1996), Cambridge University Press
39. G. Sierra, M.A. Martin-Delgado, arXiv:cond-mat/9811170v3, 1998.
40. Briegel H.J., Dur W., Cirac J.I., and Zoller P. Phys. Rev. Lett. 81 (1998) 5932
41. Imada M., Fujimori A., and Tokura Y. Rev. Mod. Phys. 70 (1998) 1039
42. Fazekas P. Lecture Notes on Electron Correlation and Magnetism (1999), World Scientific
43. Wen X.G., Wilczek F., and Zee A. Phys. Rev. B39 (1989) 11413
44. Baxter B.J. Exactly Solved Models in Statistical Mechanics (1989), Academic Press
45. Kivelson S.A., Bindloss I.P., Fradkin E., Oganesyan V., Tranquada J.M., Kapitulnik A., and Howald C. Rev. Mod. Phys. 75 (2003) 1201
46. Galindo A., and Pascual P. Quantum Mechanics (1991), Springer
47. Fannes M., Nachtergaele B., and Werner R.F. Commun. Math. Phys. 144 (1992) 443-490
48. D. Perez-Garcia, F. Verstraete, J.I. Cirac, M.M. Wolf, arXiv:0707.2260v1, 2007.
49. Ardonne E., Fendley P., and Fradkin E. Ann. Phys. 310 (2004) 493
50. Verstraete F., Wolf M.M., Perez-Garcia D., and Cirac J.I. Phys. Rev. Lett. 96 (2006) 220601
51. Van den Nest M., Dur W., and Briegel H.J. Phys. Rev. Lett. 98 (2007) 117207
52. H.Q. Zhou, R. Orus, G. Vidal, arXiv:0709.4596v1, 2007.
53. Korepin V.E., Bogoliubov N.M., and Izergin A.G. Quantum Inverse Scattering Method and Correlation Functions (1997), Cambridge University Press
54. Feynman R.P., and Hibbs A.R. Quantum Mechanics and Path Integrals (1965), McGraw-Hill Co.
55. von der Linden W. Phys. Rep. 220 (1992) 53
56. Altman E., and Auerbach A. Phys. Rev. B65 (2002) 104508
57. Hastings M.B. Phys. Rev. B69 (2004) 104431
58. Morningstar C.J., and Weinstein M. Phys. Rev. Lett. 73 (1994) 1873
59. Morningstar C.J., and Weinstein M. Phys. Rev. D54 (1996) 4131
60. Takhtajan L.A. Phys. Lett. A87 (1982) 479
61. Babujian H.M. Nucl. Phys. B215 (1983) 317
62. Tsvelik A.M. Phys. Rev. B42 (1990) 10499
63. Witten E. Commun. Math. Phys. 121 (1989) 351
64. Witten E. Nucl. Phys. B322 (1989) 629
65. Witten E. Nucl. Phys. B330 (1990) 285
66. Belavin A.A., Polyakov A.M., and Zamolodchikov A.B. Nucl. Phys. (1984) 333-380
67. Moore G.W., and Seiberg N. Commun. Math. Phys. 123 (1989) 177
68. Fradkin E.H., Nayak C., Tsvelik A.M., and Wilczek F. Nucl. Phys. B516 (1998) 704
69. In: Wilczek F. (Ed). Fractional Statistics and Anyon Superconductivity (1990), World Scientific
70. Christensen N.B., Rønnow H.M., McMorrow D.F., Harrison A., Perring T.G., Enderle M., Coldea R., and Regnault L.P. G. Aeppli. PNAS. 104 (2007) 15264-15269
71. Anderson P.W. Phys. Rev. 79 (1950) 350
72. Sawatzky G.A., Geertsma W., and Haas C. J. Magn. Magn. Mater. 3 (1976) 37
73. Lauchli A., Mila F., and Penc K. Phys. Rev. Lett. 97 (2006) 087205
74. Schroeter D.F., Kapit E., Thomale R., and Greiter M. Phys. Rev. Lett. 99 (2007) 097202