Competing orders and hidden duality symmetries in two-leg spin ladder systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 22, 2006, Pages

  Lecheminant, P ^a   Totsuka, K ^b  

^a CNRS   (France)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845732679     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.224426     Document Type: Article

References (96)

1. G. Misguich and C. Lhuillier, in Frustrated Spin Systems, edited by, H. T. Diep, (World Scientific, Singapore, 2004).
2. X. G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press, London, 2004).
3. D. J. Thouless, Proc. Phys. Soc. London PPSOAU 0370-1328 10.1088/0370-1328/86/5/301 86, 893 (1965);
4. M. Roger, J. H. Hetherington, and J. M. Delrieu, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.55.1 55, 1 (1983).
5. R. Coldea, S. M. Hayden, G. Aeppli, T. G. Perring, C. D. Frost, T. E. Mason, S. W. Cheo, and Z. Fisk, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5377 86, 5377 (2001).
6. S. Brehmer, H-J. Mikeska, M. Müller, N. Nagaosa, and S. Uchida, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.329 60, 329 (1999).
7. M. Matsuda, K. Katsumata, R. S. Eccleston, S. Brehmer, and H. J. Mikeska, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.8903 62, 8903 (2000).
8. G. Misguich, B. Bernu, C. Lhuillier, and C. Waldtmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1098 81, 1098 (1998).
9. A. Läuchli, J. C. Domenge, C. Lhuillier, P. Sindzingre, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.137206 95, 137206 (2005).
10. S-C. Zhang, Science SCIEAS 0036-8075 10.1126/science.275.5303.1089 275, 1089 (1997).
11. E. Demler, W. Hanke, and S-C. Zhang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.909 76, 909 (2004).
12. M. Hermele, T. Senthil, and M. P. A. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.104404 72, 104404 (2005).
13. D. Podolsky, E. Altman, T. Rostunov, and E. Demler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.246402 93, 246402 (2004).
14. S. Sachdev, Science SCIEAS 0036-8075 10.1126/science.288.5465.475 288, 475 (2000).
15. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science SCIEAS 0036-8075 10.1126/science.1091806 303, 1490 (2004);
16. T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.144407 70, 144407 (2004).
17. H.-H. Lin, L. Balents, and M. P. A. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.1794 58, 1794 (1998).
18. R. Konik, F. Lesage, A. W. W. Ludwig, and H. Saleur, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.4983 61, 4983 (2000);
19. R. Konik and A. W. W. Ludwig, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.155112 64, 155112 (2001).
20. H. J. Schulz, cond-mat/9808167 (unpublished).
21. H. C. Lee, P. Azaria, and E. Boulat, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.155109 69, 155109 (2004).
22. D. Controzzi and A. M. Tsvelik, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.035110 72, 035110 (2005).
23. E. Boulat, P. Azaria, and P. Lecheminant (unpublished).
24. E. Dagotto and T. M. Rice, Science SCIEAS 0036-8075 10.1126/science.274. 5287.618 271, 618 (1996).
25. I. Affleck, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/1/19/001 1, 3047 (1989).
26. H.-J. Mikeska and A. K. Kolezhuk, Lecture Notes in Physics Vol. 645, (2004) p. 1.
27. P. Lecheminant, in Frustrated Spin Systems, edited by, H. T. Diep, (World Scientific, Singapore, 2004).
28. A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.3939 78, 3939 (1997).
29. M. Müller, T. Vekua, and H-J. Mikeska, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.134423 66, 134423 (2002).
30. K. Hijii, S. Qin, and K. Nomura, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.134403 68, 134403 (2003).
31. V. Gritsev, B. Normand, and D. Baeriswyl, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.094431 69, 094431 (2004).
32. A. Läuchli, G. Schmid, and M. Troyer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.100409 67, 100409 (R) (2003).
33. T. Hikihara, T. Momoi, and X. Hu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.087204 90, 087204 (2003).
34. X. G. Wen, F. Wilczek, and A. Zee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.11413 39, 11413 (1989).
35. R. B. Laughlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60. 2677 60, 2677 (1988).
36. T. Momoi, T. Hikihara, M. Nakamura, and X. Hu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.174410 67, 174410 (2003).
37. A. F. Andreev and I. A. Grishchuk, Sov. Phys. JETP SPHJAR 0038-5646 60, 267 (1984).
38. A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University press, Cambridge, UK, 1998).
39. T. Giamarchi, Quantum Physics in One Dimension (Clarendon, Oxford, UK, 2004).
40. D. C. Cabra and P. Pujol, Lecture Notes in Physics Vol. 645, (2004), p. 253.
41. P. Lecheminant and K. Totsuka, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.020407 71, 020407 (R) (2005).
42. For a recent review, see, for instance M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen De, and U. Sen, cond-mat/0606771 (unpublished).
43. Y. Q. Li, M. Ma, D. N. Shi, and F. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3527 81, 3527 (1998).
44. Y. Yamashita, N. Shibata, and K. Ueda, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.9114 58, 9114 (1998).
45. K. I. Kugel' and D. I. Khomskii, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1982v025n04ABEH004537 25, 231 (1982).
46. S. K. Pati, R. R. P. Singh, and D. I. Khomskii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5406 81, 5406 (1998).
47. T. Barnes, E. Dagotto, J. Riera, and E. S. Swanson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.3196 47, 3196 (1993).
48. A. K. Kolezhuk and H-J. Mikeska, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2709 80, 2709 (1998);
49. A. K. Kolezhuk and H-J. Mikeska, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979298001356 12, 2325 (1998).
50. B. Sutherland, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12.3795 12, 3795 (1975).
51. Y. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.9236 60, 9236 (1999).
52. J. Timonen and A. Luther, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/18/7/011 18, 1439 (1985).
53. H. J. Schulz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.6372 34, 6372 (1986).
54. G. V. Uimin, JETP Lett. JTPLA2 0021-3640 12, 225 (1970);
55. C. K. Lai, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1666522 15, 1675 (1974).
56. T. Sakai and Y. Hasegawa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.48 60, 48 (1999).
57. G. Albertini, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.094416 64, 094416 (2001).
58. I. Affleck, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90117-4 305, 582 (1988).
59. P. Azaria, A. O. Gogolin, P. Lecheminant, and A. A. Nersesyan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.624 83, 624 (1999);
60. P. Azaria, E. Boulat, and P. Lecheminant, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.12112 61, 12112 (2000).
61. C. Itoi, S. Qin, and I. Affleck, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.6747 61, 6747 (2000).
62. J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, UK, 1996), Chap..
63. W. Chen, M-S. Chang, H-H. Lin, D. Chang, and C-Y. Mou, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.205413 70, 205413 (2004);
64. H-H. Lin, cond-mat/0010011 (unpublished).
65. D. J. Gross and A. Neveu, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.10.3235 10, 3235 (1974).
66. A. B. Zamolodchikov and Al. B. Zamolodchikov, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(79)90391-9 120, 253 (1979).
67. For a review, see, for instance, F. H. L. Essler and R. M. Konik, in From Fields to Strings: Circumnavigating Theoretical Physics, edited by, M. Shifman,,, A. Vainshtein,, and, J. Wheather, (World Scientific, Singapore, 2005).
68. T. Kennedy and H. Tasaki, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.304 45, 304 (1992).
69. N. Andrei and J. H. Lowenstein, Phys. Lett. PYLBAJ 0370-2693 10.1016/0370-2693(80)90061-1 90B, 106 (1980).
70. D. Boyanovsky and R. Holman, Nucl. Phys. B NUPBBO 0550-3213 358, 619 (1991).
71. G. Sierra and E. H. Kim, J. Phys. A JPHAC5 0305-4470 36, L37 (2003).
72. P. Lecheminant, A. O. Gogolin, and A. A. Nersesyan, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(02)00474-1 639 [FS], 502 (2002).
73. In fact, this argument can be generalized to SU (N).
74. For the details, see P. Lecheminant and K. Totsuka, cond-mat/0610254 (unpublished).
75. N. Andrei and C. Destri, Nucl. Phys. B NUPBBO 0550-3213 231, 445 (1984).
76. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987);
77. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218021 115, 477 (1988).
78. S. Sachdev, T. Senthil, and R. Shankar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.258 50, 258 (1994).
79. K. Damle and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4412 76, 4412 (1996).
80. K. Totsuka, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050494 5, 705 (1998).
81. G. I. Japaridze and A. A. Nersesyan, JETP Lett. JTPLA2 0021-3640 27, 334 (1978);
82. V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.42.65 42, 65 (1979).
83. S. Zhang and D. P. Arovas, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.2708 40, 2708 (1989). The exact hole motion observed here was rediscovered by Kolezhuk and Mikeska (see Ref. cited above) in the context of ladder systems.
84. Y. Nishiyama and M. Suzuki, Physica B PHYBE3 0921-4526 225, 41 (1996).
85. A. Klümper, A. Schadschneider, and J. Zittartz, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01309281 87, 281 (1992);
86. A. Klümper, A. Schadschneider, and J. Zittartz, Europhys. Lett. EULEEJ 0295-5075 24, 293 (1993).
87. K. Totsuka and M. Suzuki, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/7/8/012 7, 1639 (1995).
88. T. Giamarchi and H. J. Schulz, J. Phys. (Paris) JOPQAG 0302-0738 49, 819 (1988).
89. T. L. Ho, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.742 81, 742 (1998);
90. T. Ohmi and K. Machida, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.1822 67, 1822 (1998);
91. E. Demler and F. Zhou, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.163001 88, 163001 (2002);
92. A. Imambekov, M. Lukin, and E. Demler, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.063602 68, 063602 (2003).
93. R. Assaraf, P. Azaria, M. Caffarel, and P. Lecheminant, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.2299 60, 2299 (1999).
94. I. Affleck, D. Gepner, H. J. Schulz, and T. Ziman, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/5/015 22, 511 (1989);
95. R. R. P. Singh, M. E. Fisher, and R. Shankar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.2562 39, 2562 (1989).
96. K. Majumdar and M. Mukherjee, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/38/101 35, L543 (2002).