Algebraic approach to interacting quantum systems

Advances in Physics

Volumn 53, Issue 1, 2004, Pages 1-82

  Batista, C D ^a   Ortiz, G ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTER PROGRAMMING LANGUAGES; CONFORMAL MAPPING; EQUIVALENCE CLASSES; MATHEMATICAL MODELS; PHASE DIAGRAMS; THEOREM PROVING;

EMERGENT SYMMETRY; HIERARCHICAL LANGUAGES; ISOMORPHISMS; QUANTUM INFORMATION; QUANTUM PROGRAMMING LANGUAGES; QUANTUM SYSTEMS;

QUANTUM THEORY;

EID: 1542648325     PISSN: 00018732     EISSN: None     Source Type: Journal    
DOI: 10.1080/00018730310001642086     Document Type: Article

References (91)

1. Anderson, P. W., 1972, Science, 177, 393.
2. Wen, X.-G., 2002, Phys. Rev. B, 65, 165 113.
3. Jordan, P., and Wigner, E., 1928, Z. Phys., 47, 631.
4. Matsubara, T., and Matsuda, H., 1956, Prog. Theor. Phys., 16, 569.
5. Ushveridze, A. G. 1994, Quasi-Exactly Solvable Models in Quantum Mechanics (Bristol: IOP).
6. Batista, C. D., and Ortiz, G., 2000, Phys. Rev. Lett. 85, 4755.
7. Landau, L. D., and Lifshitz, E. M., 2001, Statistical Physics (Oxford: Butterworth-Heinemann).
8. Anderson, P. W., 1992, Basic Notions of Condensed Matter Physics (Redwood City: Addison-Wesley).
9. Majumdar, C. K., and Gosh, D. K., 1969, J. math. Phys., 10, 1388.
10. Majumdar, C. K., and Gosh, D. K., 1969, J. math. Phys., 10, 1399.
11. Majumdar, C. K., 1970, J. phys. C, 3, 911.
12. Shastry, B. S., and Sutherland, B., 1981, Physica B & C, 108, 1069.
13. Shastry, B. S., and Sutherland, B., 1981, Phys. Rev. Lett., 47, 964.
14. Sutherland, B., and Shastry, B. S., 1983, J. stat. Phys., 33, 477.
15. Lin, H. Q., Shen, J. L., and Shuk, H. Y. cond-mat/0109027.
16. Papanicolau, N., 1986, Phys. Lett. A 116, 89.
17. Papanicolau, N., 1988, Nucl. Phys., 305, 367.
18. Nielsen, M. A., and Chuang, I. L., 2000, Quantum Computation and Information (Cambridge: Cambridge University Press).
19. Ortiz, G., Gubernatis, J. E., Knill, E., and Laflamme, R., 2001, Phys. Rev. A, 64, 22319.
20. Bohm, A., 1993, Quantum Mechanics: Foundations and Applications (New York: Springer-Verlag).
21. Jacobson, N., 1985, Basic Algebra I (New York: W. H. Freeman).
22. Jacobson, N., 1989, Basic Algebra II (New York: W. H. Freeman).
23. Batista, C. D., and Ortiz, G., 2001, Phys. Rev. Lett., 86, 1082.
24. Zhang, S.-C., 1997, Science, 275, 1089.
25. Cornwell, J. F., 1989, Group Theory in Physics (London: Academic Press).
26. Ortiz, G., and Batista, C. D., 2002, in Recent Progress in Many-Body Theories, Raymond F. Bishop, Tobias Brandes, Klaus A. Gernoth, Niels R. Walet, and Yang Xian (eds) (Singapore: World Scientific), p. 425.
27. Ortiz, G., and Batista, C. D., 2003, Int. J. modern Phys. B, 17, 5413.
28. Fradkin, E., 1989, Phys. Rev. Lett., 63, 322.
29. Eliezer, D., and Semenoff, G. W., 1992, Phys. Lett. B, 286, 118.
30. Wang, Y. R., 1991, Phys. Rev. B, 43, 3786.
31. Huerta, L., and Zanelli, J., 1993, Phys. Rev. Lett., 71, 3622.
32. Wang, S., 1995, Phys. Rev. E, 51, 1004.
33. Green, H. S., 1953, Phys. Rev., 90, 270.
34. Batista, C. D., and Ortiz, G., 2001, in Condensed Matter Theories, vol. 16, Susana Hernandez and W. John Clark (eds) (Huntington, New York: Nova Science Publishers), p. 1.
35. Huang, K., 1963, Statistical Mechanics (New York: Wiley), Chapter 16.
36. Gentile, G., 1940, Nuovo Cimento, 17, 493.
37. Khare, A., 1997, Fractional Statistics and Quantum Theory (Singapore: World Scientific).
38. Haldane, F. D. M., 1991, Phys. Rev. Lett., 67, 937.
39. Greenberg, O. W., 1964, Phys. Rev. Lett., 13, 598.
40. Green, H. S., 1972, Prog. Theor. Phys., 47, 1400.
41. Kamefuchi, S., and Takahashi, Y., 1962, Nucl. Phys., 36, 177.
42. Ryan, C., and Sudarshan, E. C. G., 1963, Nucl. Phys., 47, 207.
43. Kademova, K., 1970, Nucl. Phys. B, 15, 350.
44. Bracken, A. J., and Green, H. S., 1972, Nuovo Cimento, 9, 349.
45. Batista, C. D., Ortiz, G., and Gubernatis, J. E., 2002, Phys. Rev. B, 65, 180 402(R).
46. Baxter, R. J., 1990, Exactly Solved Models in Statistical Mechanics (London: Academic Press).
47. Lai, C. K., 1974, J. math. Phys., 15, 1675.
48. Sutherland, B., 1975, Phys. Rev. B, 12, 3795.
49. Takhtajan, L. A., 1982, Phys. Lett. A 87, 479.
50. Babujian, H. M., 1982, Phys. Lett. A, 90, 479.
51. Babujian, H. M., 1983, Nucl. Phys. B, 215, 317.
52. Affleck, I., Kennedy, T., Lieb, E. H., and Tasaki, H., 1987, Phys. Rev. Lett., 59, 799.
53. Klüper, A., 1989, Europhys. Lett., 9, 815.
54. Arrachea, L., and Aligia, A. A., 1994, Phys. Rev. Lett., 73, 2240.
55. Sutherland, B., 2000, Phys. Rev. B, 62, 11499.
56. Mattis, D. C., and Nam, S. B., 1972, J. math. Phys., 13, 1185.
57. Lieb, E. H., and Wu, F. Y., 1968, Phys. Rev. Lett., 20, 1443.
58. Auerbach, A., 1994, Interacting Electrons and Quantum Magnetism (New York: Springer-Verlag).
59. Anderson, P. W., 1958, Phys. Rev., 110, 827.
60. Anderson, P. W., 1958, Phys. Rev., 112, 1900.
61. Ortiz, G., and Batista, C. D., 2003, Phys. Rev. B, 67, 134 301.
62. Martin, P. A., 1982, Nuovo Cimento, 68B, 302.
63. Kumar, B., 2002, Phys. Rev. B, 66, 024406.
64. Batista, C. D., and Shastry, B. S., 2003, Phys. Rev. Lett., 91, 116 401.
65. Noziéres, Ph., 1997, Theory of Interacting Fermi Systems (Reading: Addison-Wesley).
66. Ha, Z. N. C., 1996, Quantum Many-Body Systems in One Dimension (Singapore: World Scientific).
67. Solyom, J., 1987, Phys. Rev. B, 36, 8642.
68. Parkinson, J. B., 1988, J. phys. C, 21, 3793.
69. Barber, M. N., and Batchelor, M. T., 1989, Phys. Rev. B, 40, 4621.
70. Klümper, A., 1989, Europhys. Lett., 9, 815.
71. Klümper, A., 1990, J. phys. A, 23, 809.
72. Chubukov, A. V., 1990, J. phys. Condens. Matter, 2, 1593.
73. Chubukov, A. V., 1991, Phys. Rev. B, 43, 3337.
74. Fáth, G., and Sólyom, J., 1991, Phys. Rev. B, 44, 11836.
75. Fáth, G., and Sólyom, J., 1993, Phys. Rev. B, 47, 872.
76. Xiang, T., and Gehring, G. A., 1993, Phys. Rev. B, 48, 303.
77. Xian, Y., 1993, J. phys. Condens. Matter, 5, 7489.
78. Xian, Y., 1993, J. phys. Lett. A, 183, 437.
79. Fáth, G., and Sólyom, J., 1995, Phys. Rev. B, 51, 3620.
80. Montvay, I., and Münster, G., 1994, Quantum Fields on a Lattice (Cambridge: Cambridge University Press).
81. Wiese, U.-J., 1999, Nucl. Phys. B., 73, 146 and references therein.
82. Horn, D., 1981, Phys. Lett. B, 100, 149.
83. Chandrasekharan, S., and Wiese, U.-J., hep-lat/9609042.
84. Orland, P., 1992, Nucl. Phys. B, 372, 635.
85. Orlando, P., 1994, Phys. Rev. B, 49, 3423.
86. Rokhsar, D. S., and Kivelson, S. A., 1988, Phys. Rev. Lett., 61, 2376.
87. Ortiz, G., Knill, E., and Gubernatis, J. E., 2002, Nucl. Phys. B, 106, 151.
88. Somma, R., Ortiz, G., Gubernatis, J. E. Laflamme, R. and Knill, E., 2002, Phys. Rev. A, 65, 42 323
89. Somma, R., Ortiz, G., Knill, E., and Gubernatis, J. E., 2003, Int. J. quant. Inf., 1, 189.
90. Greiner, M. et al. 2002, Nature, 415, 39.
91. Barnum, H., Knill, E., Ortiz, G., and Viola, L., 2003, Phys. Rev. A, 68, 032 308. See also quantum-ph/0305023.