Low-energy properties of two-leg spin-1 antiferromagnetic ladders with commensurate external fields and their extensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 2, 2005, Pages

  Sato, Masahiro ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; BOSON; ENERGY; FERMION; MAGNET; MAGNETISM; MONTE CARLO METHOD; QUANTUM MECHANICS;

EID: 17044396245     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.024402     Document Type: Article

References (148)

1. E. Daggoto and T. M. Rice, Science 271, 618 (1996);
2. T. M. Rice, Z. Phys. B: Condens. Matter 103, 165 (1997).
3. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, and Y. Kitaoka, Phys. Rev. Lett. 73, 3463 (1994); K. Kojima, A. Keren, G. M. Luke, B. Nachumi, W. D. Wu, Y. J. Uemura, M. Azuma, and M. Takano, ibid. 74, 2812 (1995).
4. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, and Y. Kitaoka, Phys. Rev. Lett. 73, 3463 (1994); K. Kojima, A. Keren, G. M. Luke, B. Nachumi, W. D. Wu, Y. J. Uemura, M. Azuma, and M. Takano, ibid. 74, 2812 (1995).
5. Z. Honda, Y. Nonomura, and K. Katsumura, J. Phys. Soc. Jpn. 66, 3689 (1997).
6. G. Chabuoussant, M.-H. Julien, Y. Fagot-Revurat, M. Hanson, L. P. Levy, C. Berthier, M. Hovatić, and O. Piovesana, Eur. Phys. J. B 6, 167 (1998).
7. D. Arčon, A. Lappas, S. Margadonna, K. Prassides, E. Ribera, J. Veciana, C. Rovira, R. T. Henriques, and M. Almeida, Phys. Rev. B 60, 4191 (1999).
8. K. Katoh, Y. Hosokoshi, K. Inoue, and T. Goto, J. Phys. Soc. Jpn. 69, 1008 (2000); T. Goto, M. I. Bartrashevich, Y. Hosokoshi, K. Kato, and K. Inoue, Physica B 294-295, 43 (2001); T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Kato, K. Inoue, and T. Goto, ibid. 329-333, 1203 (2003); Phys. Status Solidi B 236, 429 (2003).
9. K. Katoh, Y. Hosokoshi, K. Inoue, and T. Goto, J. Phys. Soc. Jpn. 69, 1008 (2000); T. Goto, M. I. Bartrashevich, Y. Hosokoshi, K. Kato, and K. Inoue, Physica B 294-295, 43 (2001); T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Kato, K. Inoue, and T. Goto, ibid. 329-333, 1203 (2003); Phys. Status Solidi B 236, 429 (2003).
10. K. Katoh, Y. Hosokoshi, K. Inoue, and T. Goto, J. Phys. Soc. Jpn. 69, 1008 (2000); T. Goto, M. I. Bartrashevich, Y. Hosokoshi, K. Kato, and K. Inoue, Physica B 294-295, 43 (2001); T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Kato, K. Inoue, and T. Goto, ibid. 329-333, 1203 (2003); Phys. Status Solidi B 236, 429 (2003).
11. K. Katoh, Y. Hosokoshi, K. Inoue, and T. Goto, J. Phys. Soc. Jpn. 69, 1008 (2000); T. Goto, M. I. Bartrashevich, Y. Hosokoshi, K. Kato, and K. Inoue, Physica B 294-295, 43 (2001); T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Kato, K. Inoue, and T. Goto, ibid. 329-333, 1203 (2003); Phys. Status Solidi B 236, 429 (2003).
12. E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).
13. M. Oshikawa and I. Affleck, Phys. Rev. Lett. 79, 2883 (1997).
14. I. Affleck and M. Oshikawa, Phys. Rev. B 60, 1038 (1999).
15. M. Tsukano and K. Nomura, J. Phys. Soc. Jpn. 67, 302 (1998).
16. A. Zheludev, E. Ressouche, S. Maslov, T. Yokoo, S. Raymond, and J. Akimitsu, Phys. Rev. Lett. 80, 3630 (1998).
17. S. Maslov and A. Zheludev, Phys. Rev. B 57, 68 (1998); Phys. Rev. Lett. 80, 5786 (1998).
18. S. Maslov and A. Zheludev, Phys. Rev. B 57, 68 (1998); Phys. Rev. Lett. 80, 5786 (1998).
19. E. Ercolessi, G. Morandi, P. Pieri, and M. Roncaglia, Phys. Rev. B 62, 14 860 (2000).
20. Y.-J. Wang, F. H. L. Essler, M. Fabrizio, and A. A. Nersesyan, Phys. Rev. B 66, 024412 (2002).
21. M. Sato and M. Oshikawa, Phys. Rev. B 69, 054406 (2004).
22. D. Sénéchal, Phys. Rev. B 52, 15 319 (1995).
23. D. Allen and D. Sénéchal, Phys. Rev. B 61, 12 134 (2000).
24. S. Todo, M. Matsumoto, C. Yasuda, and H. Takayama, Phys. Rev. B 64, 224412 (2001).
25. For example, see F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983); E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991); A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994), and Ref. 7.
26. For example, see F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983); E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991); A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994), and Ref. 7.
27. For example, see F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983); E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991); A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994), and Ref. 7.
28. M. Matsumoto (private communication, 2004).
29. M. Matsumoto, S. Todo, M. Nakamura, C. Yasuda, and H. Takayama, Physica B 329-333, 1010 (2003).
30. In the paper, a RVB state means a linear combination of the tensor products, each of which is constructed by a dimer covering (the dimer is the singlet of a spin-2 pair). "Short-range" implies that all the bonds consist of two nearest neighboring sites.
31. E. Witten, Commun. Math. Phys. 92, 455 (1984).
32. I. Affleck, Nucl. Phys. B 265, 409 (1986).
33. I. Affleck and F. D. M. Haldane, Phys. Rev. B 36, 5291 (1987).
34. A. M. Tsvelik, Phys. Rev. B 42, 10 499 (1990).
35. D. G. Shelton, A. A. Nersesyan, and A. M. Tsvelik, Phys. Rev. B 53, 8521 (1996).
36. S. R. White, R. M. Noack, and D. J. Scalapino, Phys. Rev. Lett. 73, 886 (1994).
37. S. R. White, Phys. Rev. B 53, 52 (1996).
38. Y. Nishiyama, N. Hatano, and M. Suzuki, J. Phys. Soc. Jpn. 64, 1967 (1995).
39. G. Sierra and M. A. Martín-Delgado, Phys. Rev. B 56, 8774 (1997).
40. E. H. Kim, G. Fáth, J. Sólyom, and D. J. Scalapino, Phys. Rev. B 62, 14 965 (2000).
41. D. C. Cabra, A. Honecker, and P. Pujol, Phys. Rev. Lett. 79, 5126 (1997).
42. D. C. Cabra, A. Honecker, and P. Pujol, Phys. Rev. B 58, 6241 (1998).
43. F. Mila, Eur. Phys. J. B 6, 201 (1998).
44. A. Furusaki and S. C. Zhang, Phys. Rev. B 60, 1175 (1999).
45. T. Hikihara and A. Furusaki, Phys. Rev. B 63, 134438 (2001).
46. A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, England, 1998).
47. P. D. Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (Springer-Verlag, New York, 1997).
48. V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979).
49. H. J. Schulz, Phys. Rev. B 22, 5274 (1980).
50. R. Chitra and T. Giamarchi, Phys. Rev. B 55, 5816 (1997).
51. S. M. Bhattacharjee and S. Mukherji, J. Phys. A 31, L695 (1998).
52. F. D. M. Haldane, Phys. Rev. Lett. 47, 1840 (1981); J. Phys. C 14, 2585 (1981).
53. F. D. M. Haldane, Phys. Rev. Lett. 47, 1840 (1981); J. Phys. C 14, 2585 (1981).
54. I. Affleck, in Champs, Cordes et Phenomenes Critiques; Fields, Strings and Critical Phenomena, edited by E. Brézin and J. Zinn-Justin (Elsevier, Amsterdam, 1989), p. 564.
55. Bosonization, edited by M. Stone (World Scientific, Singapore, 1994).
56. J. v. Delft and H. Schoeller, Ann. Phys. (Leipzig) 4, 225 (1998).
57. D. Sénéchal, cond-mat/9908262 (unpublished).
58. H. J. Schulz, G. Cuniberti, and P. Fieri, in Field Theories for Low-Dimensional Condensed Matter Systems, edited by G. Morandi et al. (Springer-Verlag, New York, 2000).
59. E. Abdalla, M. Cristina, B. Abdalla, and K. D. Rothe, Non-Perturbative Methods in 2 Dimensional Quantum Field Theory, 2nd ed. (World Scientific, Singapore, 2001).
60. K. Ide, M. Nakamura, and M. Sato, 58th Annual Meeting of the Physical Society of Japan, 2003.
61. K. Nomura and A. Kitazawa, cond-mat/0201072 (unpublished).
62. M. Nakamura and J. Voit, Phys. Rev. B 65, 153110 (2002); M. Nakamura and S. Todo, Phys. Rev. Lett. 89, 077204 (2002).
63. M. Nakamura and J. Voit, Phys. Rev. B 65, 153110 (2002); M. Nakamura and S. Todo, Phys. Rev. Lett. 89, 077204 (2002).
64. K. Okamoto, N. Okazaki, and T. Sakai, J. Phys. Soc. Jpn. 70, 636 (2001).
65. For example, see Refs. 34, 60, and 70.
66. (cr)=0. 695.
67. K. Okamoto, K. Okunishi, and T. Sakai (in preparation).
68. In this paper, we say the phase transition is of a BKT type, only when it can be regarded as the transition of the (1 + 1)D sine-Gordon model that the marginal relevant sin term becomes marginal irrelevant or vice-versa. Since in a particle language, the chemical potential changes when the magnetization (or uniform field) is changed, the effective theory near the transition occurring with increasing (decreasing) the magnetization will become a misfit sine-Gordon model rather than a simple sine-Gordon model.
69. M. Oshikawa, M. Yamanaka, and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997).
70. F. C. Alcaraz and A. L. Malvezzi, J. Phys. A 28, 1521 (1995).
71. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, England, 1993).
72. M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, Cambridge, England, 1999).
73. S. Eggert, I. Affleck, and M. Takahashi, Phys. Rev. Lett. 73, 332 (1994).
74. This is reliable near the level-crossing line considered.
75. Of course, it is possible to obtain the result (21) from the formula (19).
76. The bosonization can lead to the same gap behavior, too, although the spin-wave analysis is simpler and exact.
77. cr enough.
78. S. Lukyanov and A. Zamolodchikov, Nucl. Phys. B 493, 571 (1997).
79. S. Lukyanov, Mod. Phys. Lett. A 12, 2543 (1997).
80. T. Hikihara and A. Furusaki, Phys. Rev. B 69, 064427 (2004).
81. G. Sierra, J. Phys. A 29, 3299 (1996); cond-mat/9610057 (unpublished).
82. Besides these two, Schulz's method based on the Abelian bosonization [see H. J. Schulz, Phys. Rev. B 34, 6372 (1986)] are often used in high spin systems. However, its starting point, the spin-1/2 XY chain, is far from the SU(2) Heisenberg point considered now.
83. T. Inami and S. Odake, Phys. Rev. Lett. 70, 2016 (1993).
84. A. Kitazawa and K. Nomura, Phys. Rev. B 59, 11 358 (1998).
85. L. Takhtajan, Phys. Lett. 87A, 479 (1982).
86. J. Babujian, Phys. Lett. 90A, 479 (1982); Nucl. Phys. B 215, 317 (1983).
87. J. Babujian, Phys. Lett. 90A, 479 (1982); Nucl. Phys. B 215, 317 (1983).
88. In Refs. 82 and 85, the fine reviews are found.
89. J. Sólyom, Phys. Rev. B 36, 8642 (1987).
90. T. Kennedy, J. Phys.: Condens. Matter 2, 5737 (1990).
91. G. Path and J. Solyom, Phys. Rev. B 44, 11 836 (1991); J. Phys.: Condens. Matter 5, 8983 (1993); Phys. Rev. B 47, 872 (1993); 51, 3620 (1995).
92. G. Path and J. Solyom, Phys. Rev. B 44, 11 836 (1991); J. Phys.: Condens. Matter 5, 8983 (1993); Phys. Rev. B 47, 872 (1993); 51, 3620 (1995).
93. G. Path and J. Solyom, Phys. Rev. B 44, 11 836 (1991); J. Phys.: Condens. Matter 5, 8983 (1993); Phys. Rev. B 47, 872 (1993); 51, 3620 (1995).
94. G. Path and J. Solyom, Phys. Rev. B 44, 11 836 (1991); J. Phys.: Condens. Matter 5, 8983 (1993); Phys. Rev. B 47, 872 (1993); 51, 3620 (1995).
95. R. J. Bursill, T. Xiang, and G. A. Gehring, J. Phys. A 28, 2109 (1995).
96. U. Schollwöck, Th. Jolicoeur, and T. Garel, Phys. Rev. B 53, 3304 (1996).
97. A. Schmitt, K-H. Mütter, M. Karbach, Y. Yu, and G. Müller, Phys. Rev. B 58, 5498 (1998).
98. O. Golinelli, Th. Jolicoeur, and E. S. Sørensen, Eur. Phys. J. B 11, 199 (1999).
99. G. Fáth and A. Süto, Phys. Rev. B 62, 3778 (2000).
100. K. Nomura, J. Phys. Soc. Jpn. 72, 476 (2003).
101. A. Läuchli, G. Schmid, and S. Trebst, cond-mat/0311082 (unpublished).
102. C. K. Lai, J. Math. Phys. 15, 1675 (1974); B. Sutherland, Phys. Rev. B 12, 3795 (1975).
103. C. K. Lai, J. Math. Phys. 15, 1675 (1974); B. Sutherland, Phys. Rev. B 12, 3795 (1975).
104. F. C. Alcaraz and M. J. Martins, J. Phys. A 21, L381 (1988); 21, 4397 (1988).
105. F. C. Alcaraz and M. J. Martins, J. Phys. A 21, L381 (1988); 21, 4397 (1988).
106. I. Affleck, D. Geppner, H. J. Shultz, and T. Zimann, J. Phys. A 2, 511 (1989).
107. L. V. Avdeev, J. Phys. A 23, L485 (1990).
108. C. Itoi and H. Mukaida, J. Phys. A 27, 4695 (1994).
109. C. Itoi and M. H. Kato, Phys. Rev. B 55, 8295 (1997).
110. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987); Commun. Math. Phys. 115, 477 (1988).
111. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987); Commun. Math. Phys. 115, 477 (1988).
112. I. Affleck, Phys. Rev. Lett. 56, 2763 (1986).
113. A. B. Zamolodchikov and V. A. Fateev, Yad. Fiz. 43, 1031 (1986) [Sov. J. Nucl. Phys. 43, 657 (1986)].
114. A. B. Zamolodchikov and V. A. Fateev, Yad. Fiz. 43, 1031 (1986) [Sov. J. Nucl. Phys. 43, 657 (1986)].
115. D. C. Cabra, P. Pujol, and C. von Reichenbach, Phys. Rev. B 58, 65 (1998).
116. 0) is relevant, too. However, it is translated into fermionic operators through the operator product expansions of the c=1/2 CFT [see Eq. (30) and Appendix B 2],
117. Generally, the effective theory, derived from a lattice model as a continuum limit, has higher symmetries than the lattice model. Hence, sometimes symmetries of the lattice do not uniquely associate with one of the effective theory. In our case, there may exist more suitable correspondences than those we adopt here.
118. M. Takahashi, Phys. Rev. Lett. 62, 2313 (1989).
119. T. Sakai and M. Takahashi, Phys. Rev. B 42, 1090 (1990); J. Phys. Soc. Jpn. 60, 760 (1991); 60, 3615 (1991); Phys. Rev. B 43, 13383 (1991).
120. T. Sakai and M. Takahashi, Phys. Rev. B 42, 1090 (1990); J. Phys. Soc. Jpn. 60, 760 (1991); 60, 3615 (1991); Phys. Rev. B 43, 13383 (1991).
121. T. Sakai and M. Takahashi, Phys. Rev. B 42, 1090 (1990); J. Phys. Soc. Jpn. 60, 760 (1991); 60, 3615 (1991); Phys. Rev. B 43, 13383 (1991).
122. T. Sakai and M. Takahashi, Phys. Rev. B 42, 1090 (1990); J. Phys. Soc. Jpn. 60, 760 (1991); 60, 3615 (1991); Phys. Rev. B 43, 13383 (1991).
123. I. Affleck, Phys. Rev. B 41, 6697 (1990); 43, 3215 (1991).
124. I. Affleck, Phys. Rev. B 41, 6697 (1990); 43, 3215 (1991).
125. E. S. Sørensen and I. Affleck, Phys. Rev. Lett. 71, 1633 (1993).
126. R. M. Konik and P. Fendley, Phys. Rev. B 66, 144416 (2002).
127. G. Fáth, Phys. Rev. B 68, 134445 (2003).
128. S. Todo and K. Kato, Phys. Rev. Lett. 87, 047203 (2001).
129. T. T. Wu, B. McCoy, C. A. Tracy, and E. Barouch, Phys. Rev. B 13, 316 (1976).
130. A. A. Nersesyan, A. O. Gogolin, and F. H. L. Eßler, Phys. Rev. Lett. 81, 910 (1998).
131. Note that the RG equations do not contain renormalizations of fields and velocities.
132. J. L. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge. England, 1996).
133. L. Balents and M. P. A. Fisher, Phys. Rev. B 53, 12 133 (1996).
134. D. Allen and D. Sénéchal, Phys. Rev. B 55, 299 (1997).
135. M. Nakamura, Physica B 329-333, 1000 (2003).
136. M. Kohmoto and H. Tasaki, Phys. Rev. B 46, 3486 (1992).
137. A. B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43, 565 (1986) [JETP Lett. 43, 730 (1986)]; Yad. Fiz. 46, 1819 (1987) [Sov. I. Nucl. Phys. 46, 1090 (1987)].
138. A. B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43, 565 (1986) [JETP Lett. 43, 730 (1986)]; Yad. Fiz. 46, 1819 (1987) [Sov. I. Nucl. Phys. 46, 1090 (1987)].
139. A. B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43, 565 (1986) [JETP Lett. 43, 730 (1986)]; Yad. Fiz. 46, 1819 (1987) [Sov. I. Nucl. Phys. 46, 1090 (1987)].
140. A. B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43, 565 (1986) [JETP Lett. 43, 730 (1986)]; Yad. Fiz. 46, 1819 (1987) [Sov. I. Nucl. Phys. 46, 1090 (1987)].
141. M. Fabrizio, A. O. Gogolin, and A. A. Nersesyan, Nucl. Phys. B 580, 647 (2000).
142. B. K. Chakrabarti, A. Dutta, and P. Sen, Quantum Ising Phases and Transitions in Transverse Ising Models (Springer-Verlag, Berlin, 1996).
143. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001).
144. I. B. Kogut, Rev. Mod. Phys. 51, 659 (1979).
145. D. Boyanovsky, Phys. Rev. B 39, 6744 (1989).
146. C. Itzykson and J-M. Druffe, Statistical Field Theory, Vols. 1 and 2 (Cambridge University Press, Cambridge, 1991).
147. P. D. Francesco, H. Saleur, and J. B. Zuber, Nucl. Phys. B 290, 527 (1987).
148. G. Delfino and G. Mussardo, Nucl. Phys. B 516, 675 (1998).