Valence bond solids for SU (n) spin chains: Exact models, spinon confinement, and the Haldane gap

Physical Review B - Condensed Matter and Materials Physics

Volumn 75, Issue 18, 2007, Pages

  Greiter, Martin ^a   Rachel, Stephan ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34347340707     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.75.184441     Document Type: Article

References (86)

1. H. Bethe, Z. Phys. ZEPYAA 0044-3328 10.1007/BF01341708 71, 205 (1931)
2. translated in The Many-Body Problem, edited by, D. C. Mattis, (World Scientific, Singapore, 1993).
3. C. N. Yang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.19.1312 19, 1312 (1967).
4. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1990).
5. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, 1997).
6. L. D. Faddeev and L. A. Takhtajan, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(81)90335-2 85A, 375 (1981).
7. R. B. Laughlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50. 1395 50, 1395 (1983).
8. Quantum Hall Effect, edited by, M. Stone, (World Scientific, Singapore, 1992).
9. F. D. M. Haldane, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(83) 90631-X 93A, 464 (1983).
10. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 50.1153 50, 1153 (1983).
11. I. Affleck, in Fields, Strings and Critical Phenomena, edited by, E. Brézin, and, J. Zinn-Justin,, Les Houches lectures Vol. XLIX (Elsevier, Amsterdam, 1990).
12. E. Fradkin, Field Theories of Condensed Matter Systems, Frontiers in Physics No. 82 (Westview, Boulder, Co, 1991).
13. A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, 1998).
14. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).
15. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664979 10, 1399 (1969).
16. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987).
17. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218021 115, 477 (1988).
18. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 60.635 60, 635 (1988).
19. B. S. Shastry, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60. 639 60, 639 (1988).
20. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 66.1529 66, 1529 (1991).
21. F. D. M. Haldane, Z. N. C. Ha, J. C. Talstra, D. Bernard, and V. Pasquier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2021 69, 2021 (1992).
22. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 67.937 67, 937 (1991).
23. Z. N. C. Ha and F. D. M. Haldane, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.12459 47, 12459 (1993).
24. F. H. L. Eßler, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51. 13357 51, 13357 (1995).
25. M. Greiter and D. Schuricht, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.224424 71, 224424 (2005).
26. M. Greiter (unpublished).
27. M. Greiter and D. Schuricht, Phys. Rev. Lett. PRLTAO 0031-9007 (to be published).
28. N. Kawakami, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.1005 46, 1005 (1992).
29. N. Kawakami, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.3191 46, R3191 (1992).
30. Z. N. C. Ha and F. D. M. Haldane, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.9359 46, 9359 (1992).
31. P. Bouwknegt and K. Schoutens, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(96)00565-2 482, 345 (1996).
32. D. Schuricht and M. Greiter, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10168-1 71, 987 (2005).
33. D. Schuricht and M. Greiter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.235105 73, 235105 (2006).
34. R. Jullien and F. D. M. Haldane, Bull. Am. Phys. Soc. BAPSA6 0003-0503 28, 344 (1983).
35. I. Affleck, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/1/19/001 1, 3047 (1989).
36. K. Okamoto and K. Nomura, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90823-5 169, 433 (1992).
37. S. Eggert, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.R9612 54, R9612 (1996).
38. S. R. White and I. Affleck, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.9862 54, 9862 (1996).
39. D. Sen and N. Surendran, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.104411 75, 104411 (2007).
40. S. Knabe, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01019721 52, 627 (1988).
41. M. Fannes, B. Nachtergaele, and R. F. Werner, Europhys. Lett. EULEEJ 0295-5075 10, 633 (1989).
42. W.-D. Freitag and E. Müller-Hartmann, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01313409 83, 381 (1991).
43. A. Klümper, A. Schadschneider, and J. Zittartz, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/16/012 24, L955 (1991).
44. T. Kennedy and H. Tasaki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.304 45, 304 (1992).
45. A. Klümper, A. Schadschneider, and J. Zittartz, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01309281 87, 281 (1992).
46. A. Klümper, A. Schadschneider, and J. Zittartz, Europhys. Lett. EULEEJ 0295-5075 24, 293 (1993).
47. M. T. Batchelor and C. M. Yung, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S021797929400155X 8, 3645 (1994).
48. U. Schollwöck, T. Jolicoeur, and T. Garel, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.3304 53, 3304 (1996).
49. A. Kolezhuk, R. Roth, and U. Schollwöck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.5142 77, 5142 (1996).
50. A. K. Kolezhuk and U. Schollwöck, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.100401 65, 100401 (R) (2002).
51. B. Normand and F. Mila, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.104411 65, 104411 (2002).
52. A. Läuchli, G. Schmid, and S. Trebst, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.144426 74, 144426 (2006).
53. B. Sutherland, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12.3795 12, 3795 (1975).
54. T. C. Choy and F. D. M. Haldane, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(82)90057-3 90A, 83 (1982).
55. Y. Q. Li, M. Ma, D. N. Shi, and F. C. Zhang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.12781 60, 12781 (1999).
56. S. J. Gu and Y. Q. Li, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66. 092404 66, 092404 (2002).
57. J. Damerau and A. Klümper, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 2006, 1204.
58. N. Kawashima and Y. Tanabe, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.057202 98, 057202 (2007).
59. A. Paramekanti and J. B. Marston, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/12/125215 19, 125215 (2007).
60. I. Affleck, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(86)90167-7 265, 409 (1986).
61. I. Affleck, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90117-4 305, 582 (1988).
62. S. Chen, C. Wu, S. C. Zhang, and Y. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.214428 72, 214428 (2005).
63. S. Chen, Y. Wang, W. Q. Ning, C. Wu, and H. Q. Lin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.174424 74, 174424 (2006).
64. I. Affleck and E. H. Lieb, Lett. Math. Phys. LMPHDY 0377-9017 10.1007/BF00400304 12, 57 (1986).
65. M. Greiter, S. Rachel, and D. Schuricht, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.060401 75, 060401 (R) (2007).
66. P. M. van den Broek, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(80) 90662-3 77A, 261 (1980).
67. T. Inui, Y. Tanabe, and Y. Onodera, Group Theory and Its Applications in Physics (Springer, Berlin, 1996).
68. J. F. Cornwell, Group Theory in Physics (Academic, London, 1984), Vol. II.
69. H. Georgi, Lie Algebras in Particle Physics (Addison-Wesley, Redwood City CA, 1982).
70. J. Schwinger, in Quantum Theory of Angular Momentum, edited by, L. Biedenharn, and, H. van Dam, (Academic, New York, 1965).
71. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994).
72. M. Greiter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.134443 65, 134443 (2002).
73. M. Greiter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.054505 66, 054505 (2002).
74. A. J. Macfarlane, A. Sudbery, and P. H. Weisz, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01654302 11, 77 (1968).
75. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory (Springer, New York, 1987).
76. I. Affleck, D. P. Arovas, J. B. Marston, and D. A. Rabson, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(91)90027-U B366, 467 (1991).
77. J. B. Marston and I. Affleck, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.11538 39, 11538 (1989).
78. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
79. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).
80. C. Honerkamp and W. Hofstetter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.170403 92, 170403 (2004).
81. C. Honerkamp and W. Hofstetter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.094521 70, 094521 (2004).
82. A. Rapp, G. Zaránd, C. Honerkamp, and W. Hofstetter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.160405 98, 160405 (2007).
83. L.-M. Duan, E. Demler, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.090402 91, 090402 (2003).
84. J. J. García-Ripoll, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.250405 93, 250405 (2004).
85. A. Micheli, G. K. Brennen, and P. Zoller, Nat. Phys. ZZZZZZ 1745-2473 2, 341 (2006).
86. G. K. Brennen, A. Micheli, and P. Zoller, arXiv:quant-ph/0612180 (unpublished).