Integrable models and quantum spin ladders: Comparison between theory and experiment for the strong coupling ladder compounds

Advances in Physics

Volumn 56, Issue 3, 2007, Pages 465-543

  Batchelor, M T ^a   Guan, X W ^a   Oelkers, N ^b   Tsuboi, Z ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF QUEENSLAND   (Australia)

^c OKAYAMA INSTITUTE FOR QUANTUM PHYSICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FERRIMAGNETIC MATERIALS; FREE ENERGY; MAGNETIC ANISOTROPY; MAGNETIZATION; MATHEMATICAL MODELS; PHASE TRANSITIONS; THERMAL EXPANSION;

QUANTUM SPIN LADDERS; SPIN LADDER MODELS; ZERO TEMPERATURE;

QUANTUM CHEMISTRY;

EID: 34249672304     PISSN: 00018732     EISSN: 14606976     Source Type: Journal    
DOI: 10.1080/00018730701265383     Document Type: Article

References (230)

1. J.B. McGuire, J. Math. Phys. 5 622 (1964).
2. C.N. Yang, Phys. Rev. Lett. 19 1312 (1967).
3. R.J. Baxter, Ann. Phys. N.Y. 70 193 (1972).
4. V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, 1993).
5. M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, Cambridge, 1999).
6. H.A. Bethe, Zeits. Physik 71 205 (1931).
7. M.T. Batchelor, Physics Today 60 36 (2007).
8. M.T. Batchelor, X.-W. Guan, N. Oelkers, K. Sakai, Z. Tsuboi and A. Foerster, Phys. Rev. Lett. 91 217202 (2003).
9. G.V. Uimin, JETP Lett. 12 225 (1970).
10. C.K. Lai, J. Math. Phys. 15 1675 (1974).
11. B. Sutherland, Phys. Rev. B 12 3795 (1975).
12. V.V. Bazhanov, Phys. Lett. B 159 321 (1985).
13. M. Jimbo, Comm. Math. Phys. 102 537 (1986).
14. J.H.H. Perk and C.L. Schultz, Phys. Lett. A 84 407 (1981).
15. E. Lieb, T. Schultz and D. Mattis, Ann. Phys. N.Y. 16 407 (1961).
16. F.D.M. Haldane, Phys. Lett. A 93 464 (1983).
17. F.D.M. Haldane, Phys. Rev. Lett. 50 1153 (1983).
18. T. Barnes, E. Dagotto, J. Riera and E.S. Swanson, Phys. Rev. B 47 3196 (1993).
19. E. Dagotto and T.M. Rice, Science 271 618 (1996).
20. E. Dagotto, Rep. Prog. Phys. 62 1525 (1999).
21. P. Lecheminant, in Frustrated Spin Systems, edited by H.T. Diep (World Scientific, Singapore, 2005).
22. S. Sachdev, Science 288 475 (2000).
23. S.R. White, Phys. Rev. B 53 52 (1996).
24. C.D. Batista and G. Ortiz, Adv. Phys. 53 1 (2004).
25. D.C. Johnston and J.W. Johnson, D.P. Goshorn and A.J. Jacobson, Phys. Rev. B 35 219 (1987).
26. E. Dagotto, J. Riera and D.J. Scalapino, Phys. Rev. B 45 5744 (1992).
27. D.C. Johnston, M. Troyer, S. Miyahara, D. Lidsky, K. Ueda, M. Azuma, Z. Hiroi, M. Takano, M. Isobe, Y. Ueda, M. A. Korotin, V.I. Anisimov, A.V. Mahajan and L.L. Miller, arXiv:cond-mat/0001147 (2000).
28. E.M. McCarron, M.A. Subramanian, J.C. Calabrese and R.L. Harlow, Mater. Res. Bull. 23 1355 (1988).
29. T. Siegrist, L.F. Schneemeyer, S.A. Sunshine, J.V. Waszczak and R.S. Roth, Mater. Res. Bull. 23 1429 (1988).
30. Z. Hiroi and M. Takano, Nature 377 41 (1995).
31. S.R. White, R.M. Noack and D.J. Scalapino, Phys. Rev. Lett. 73 886 (1994).
32. S. Gopalan, T.M. Rice and M. Sigrist, Phys. Rev. B 49 8901 (1994).
33. D.G. Shelton, A.A. Nersesyan and A.M. Tsvelik, Phys. Rev. B 53 8521 (1996).
34. M. Azuma, Y. Fujishiro, M. Takano, M. Nohara and H. Takagi, Phys. Rev. B 55 R8658 (1997).
35. N. Fujiwara, H. Yasuoka, Y. Fujishiro, M. Azuma and M. Takano, Phys. Rev. Lett. 80 604 (1998).
36. M. Azuma, Z. Hiroi, M. Takano, K. Ishida and Y. Kitaoka, Phys. Rev. Lett. 73 3463 (1994).
37. K. Kojima, A. Keren, G.M. Luke, B. Nachumi, W.D. Wu, Y.J. Uemura, M. Azuma and M. Takano, Phys. Rev. Lett. 74 2812 (1995).
38. K. Ishida, Y. Kitaoka, Y. Tokunaga, S. Matsumoto, K. Asayama, M. Azuma, Z. Hiroi and M. Takano, Phys. Rev. B 53 2827 (1996).
39. F. Mila, Eur. J. Phys. 21 499 (2000).
40. T.M. Rice, S. Gopalan and M. Sigrist, Europhys. Lett. 23 445 (1993).
41. M. Sigrist, T.M. Rice and F.C. Zhang, Phys. Rev. B 49 12058 (1994).
42. C.P. Landee, M.M. Turnbull C. Galeriu, J. Giantsidis and F.M. Woodward, Phys. Rev. B 63 100402 (2001).
43. B. Chiari, O. Piovesana, T. Tarantelli and P.F. Zanazzi, Inorg. Chem. 29 1172 (1990).
44. G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, L.P. Lévy, C. Berthier, M. Horvatić and O. Piovesana, Phys. Rev. Lett. 79 925 (1997).
45. G. Chaboussant, Y. Fagot-Revurat, M.-H. Julien, M.E. Hanson, C. Berthier, M. Morvatić, L.P. Lévy, and O. Piovesana, Phys. Rev. Lett. 80 2713 (1998).
46. G. Chaboussant, P.A. Crowell, L.P. Lévy, O. Piovesana, A. Madouri and D. Dailly, Phys. Rev. B 55 3046 (1997).
47. B.C. Watson, V.N. Kotov, M.W. Meisel, D.W. Hall, G.E. Granroth, W.T. Montfrooij, S.E. Nagler, D.A. Jensen, R. Backov, M.A. Petruska, G.E. Fanucci and D.R. Talham, Phys. Rev. Lett. 86 5168 (2001).
48. H. Tanaka, K. Takatsu, W. Shiramura and T. Ono, J. Phys. Soc. Japan 65 1945 (1996).
49. T. Nakamura and K. Okamoto, Phys. Rev. B 58 2411 (1998).
50. W. Shiramura, K. Takatsu, H. Tanaka, K. Kamishima, M. Takahashi, H. Mitamura and T. Goto, J. Phys. Soc. Japan 66 1900 (1997).
51. A. Oosawa, T. Takamasu, K. Tatani, H. Abe, N. Tsujii, O. Suzuki, H. Tanaka, G. Kido and K. Kindo, Phys. Rev. B 66 104405 (2002).
52. N. Cavadini, T. Henggeler, A. Furrer, H.U. Gudel, K. Kramer, H. Mutka, Eur. Phys. J. B 7 519 (1999).
53. N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.U. Gudel, K. Kramer, H. Mutka, J. Phys: Condens. Matter 12 5463 (2000).
54. N. Cavadini, D. Andreica, F.N. Gygax, A. Schenck, K. Kramer, H.U. Gudel, H. Mutka and A. Wildes, Physica B 335 37 (2003).
55. M. Müller and H.-J. Mikeska, J. Phys. Condens. Matter 12 7633 (2000).
56. M. Müller, H.-J. Mikeska and N. Cavadini, J. Phys. Condens. Matter 15 8513 (2003).
57. A. Oosawa, M. Fujisawa, T. Osakabe, K. Kakurai and H. Tanaka, J. Phys. Soc. Japan 72 1026 (2003).
58. A. Oosawa, H.A. Katori and H. Tanaka, Phys. Rev. B 63 134416 (2001).
59. M. Hagiwara, H.A. Katori, U. Schollwöck and H.-J. Mikeska, Phys. Rev. B 62 1051 (2000).
60. M. Matsumoto, B. Normand, T.M. Rice and M. Sigrist, Phys. Rev. Lett. 89 077203 (2002).
61. H. Tanaka, W. Shiramura, T. Takatsu, B. Kurniawan, M. Takahashi, K. Kamishima, K. Takizawa, H. Mitamura and T. Goto, Physica B 246-247 230 (1998).
62. K. Takatsu, W. Shiramura and H. Tanaka, J. Phys. Soc. Japan 66 1611 (1997).
63. M. Reigrotzki, H. Tsunetsugu and T.M. Rice, J. Phys.: Condens. Matter 6 9235 (1994).
64. G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, M. Hanson, L.P. Levy, C. Berthier, M. Horvatic and O. Piovesana, Eur. Phys. J. B 6 167 (1998).
65. G. Chaboussant, P.A. Crowell, L.P. Levy, O. Piovesana, A. Madouri and D. Mailly, Phys. Rev. B 55 3046 (1997).
66. M. Troyer, H. Tsunetsugu and D. Würtz, Phys. Rev. B 50 13515 (1994).
67. T. Giamarchi and A.M. Tsvelik, Phys. Rev. B 59 11398 (1999).
68. I. Affleck, Phys. Rev. B 43 3215 (1991).
69. E.S. Sorensen and I. Affleck, Phys. Rev. Lett. 71 1633 (1993).
70. A. Oosawa, M. Ishii and H. Tanaka, J. Phys. Condens. Matter 11 265 (1999).
71. T. Nikuni, M. Oshikawa, A. Oosawa and H. Tanaka, Phys. Rev. Lett. 84 5868 (2000).
72. K. Kudo, M. Yawamata, T. Noji, Y. Koike, T. Nishizaki, N. Kobayashi and H. Tanaka, J. Phys. Soc. Japan 73 2358 (2004).
73. J. Sirker, A. Weiße and O.P. Sushkov, Physica B 359-361 1318 (2005).
74. S. Miyahara and K. Ueda, Phys. Rev. Lett. 82 3701 (1999).
75. H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C.P. Slichter, T. Goto and Y. Ueda, Phys. Rev. Lett. 82 3168 (1999).
76. K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca and F. Mila, Science 298 395 (2002).
77. Y. Hosokoshi, K. Katoh,Y. Nakazawa, H. Nakano and K. Inoue, J. Am. Chem. Soc. 127 7921 (2001).
78. K. Katoh, Y. Hosokoshi, K. Inoue, M.I. Bartashevich, H. Nakano and T. Goto, J. Phys. Chem. Solids 63 1277 (2003).
79. Y. Hosokoshi, K. Katoh and K. Inoue, Synthetic Metals 133-134 527 (2003).
80. A.K. Kolezhuk and H.-J. Mikeska, Eur. Phys. J. B 5 543 (1998).
81. A. Langariand M.A. Martiń-Delgado, Phys. Rev. B 62 11725 (2000).
82. J. Lou, C. Chen and S. Qin, Phys. Rev. B 64 144403 (2001).
83. A.K. Kolezhuk, H.-J. Mikeska and S. Yamamoto, Phys. Rev. B 55 R3336 (1997).
84. A.K. Kolezhuk, H.-J. Mikeska, K. Maisinger and U. Schollwöck, Phys. Rev. B 59 13565 (1999).
85. S. Yamamoto, Phys. Rev. B 59 1024 (1999).
86. S. Yamamoto and T. Sakai, J. Phys.: Condens. Matter 11 5175 (1999).
87. S.K. Pati, S. Ramasesha and D. Sen, Phys. Rev. B 55 8894 (1997).
88. T. Sakai and K. Okamoto, Phys. Rev. B 65 214403 (2002).
89. W. Zheng and J. Oitmaa, Phys. Rev. B 67 224421 (2003).
90. M. Hagiwara, K. Minami, Y. Narumi, K. Tatani and K. Kindo,J. Phys. Soc. Japan, 67 2209 (1998).
91. A.A. Nersesyan and A.M. Tsvelik, Phys. Rev. Lett. 78 3939 (1997).
92. Y. Wang, Phys. Rev. B 60 9236 (1999).
93. A.K. Kolezhuk and H.-J Mikeska, Phys. Rev. Lett. 80 2709 (1998).
94. Y. Wang and P. Schlottmann, Phys. Rev. B 62 3845 (2000).
95. S. Cai, J. Dai and Y. Wang, Phys. Rev. B 66 134403 (2002).
96. M.T. Batchelor and M. Maslen, J. Phys. A 32 L377 (1999).
97. J. de Gier and M.T. Batchelor, Phys. Rev. B 62 R3584 (2000).
98. M.T. Batchelor, J. de Gier and M. Maslen, J Stat. Phys. 102 559 (2001).
99. M. Maslen, M.T. Batchelor and J. de Gier, Phys. Rev. B 68 024418 (2003).
100. A.A. Zvyagin, Phys. Rev. B 51 12579 (1995).
101. S. Park and K. Lee J. Phys. A 31 6569 (1998).
102. N. Muramoto and M. Takahashi, J. Phys. Soc. Japan 68 2098 (1999).
103. H. Frahm and A. Kundu, J. Phys. C: Cond. Mat. 11 L557 (1999).
104. M.T. Batchelor and M. Maslen, J. Phys. A 33 443 (2000).
105. M.T. Batchelor, J. de Gier, J. Links and M. Maslen, J. Phys. A 33 L97 (2000).
106. J. Links and A. Foerster, Phys. Rev. B 62 65 (2000).
107. A. Foerster, K.E. Hibberd, J.R. Links and I. Roditi, J. Phys. A 34 L25 (2001).
108. J. Ambjorn, D. Arnaudon, A. Sedrakyan, T. Sedrakyan and P. Sorba, J. Phys. A 34 5887 (2001).
109. S. Albeverio and S.-M. Fei, J. Phys. A 34 6545 (2001).
110. A.A. Zvyagin, J. Phys. A 34 R21 (2001).
111. A.P. Tonel, A. Foerster, J. Links, and A.L. Malvezzi, Phys. Rev. B 64 054420 (2001).
112. A.P. Tonel, A. Foerster, X.-W. Guan and J. Links, J. Phys. A 36 359 (2003).
113. V. Gritsev and D. Baeriswyl, J. Phys. A 36 12129 (2003).
114. D. Arnaudon, A. Sedrakyan and T. Sedrakyan, Int. J. Mod. Phys. A 19 16 (2004).
115. D. Arnaudon, A. Sedrakyan and T. Sedrakyan, Nucl. Phys. B 676 615 (2004).
116. M.T. Batchelor, X.-W. Guan, A. Foerster and H.-Q. Zhou,New J. Phys. 5 107 (2003).
117. M.T. Batchelor, X.-W. Guan, A. Foerster, A.P. Tonel and H.-Q. Zhou, Nucl. Phys. B 669 385 (2003).
118. F. Mila and F.C. Zhang, Eur. Phys. J. B 16 7 (2000).
119. C.N. Yang and C.P. Yang, J. Math. Phys. 10 1115 (1969).
120. M. Takahashi, Prog. Theor. Phys. 46 401 (1971).
121. C. Destri and H. J. de Vega, Nucl. Phys. B 438 413 (1995).
122. M. Takahashi, Prog. Theor. Phys. 47 69 (1972).
123. F.H.L. Essler, H. Frahm, F. Gömann, A. Klümper, V.E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press, Cambridge, 2005).
124. P. Schlottmann, Phys. Rev. B 33 4880 (1986).
125. P. Schlottmann, Int. J. Mod. Phys. B 11 355 (1997).
126. F.H.L. Essler and V.E. Korepin, Phys. Rev. B 46 9147 (1992).
127. A. Foerster and M. Karowski, Nucl. Phys. B 396 611 (1993).
128. A.M. Tsvelik and P.B. Wiegmann, Adv. Phys. 32 453 (1983).
129. M. Shiroishi and M. Takahashi, Phys. Rev. Lett. 89 117201 (2002).
130. Z. Tsuboi, Phys. Lett. B 544 222 (2002).
131. Z. Tsuboi, J. Phys. A 36 1493 (2003).
132. O. Rojas, S.M. de Souza and M.T. Thomaz, J. Math. Phys. 43 1390 (2002).
133. A. Bühler, N. Elstner and G.S. Uhrig, Eur. Phys. J B 16 475 (2000).
134. M. Suzuki, Phys. Rev. B 31 2957 (1985).
135. A. Klümper, Ann. Physik 1 540 (1992).
136. G. Jüttner, A. Klümper and J. Suzuki, Nucl. Phys. B 487 650 (1997).
137. A. Klümper, Z. Phys. B 91 507 (1993).
138. M. Suzuki and M. Inoue, Prog. Theor. Phys. 78 787 (1987).
139. T. Koma, Prog. Theor. Phys. 78 1213 (1987).
140. J. Suzuki, Y. Akutsu and M. Wadati, J. Phys. Soc. Jpn. 59 2667 (1990).
141. G. Jüttner, A. Klümper and J. Suzuki, Nucl. Phys. B 522 471 (1998).
142. A. Fujii and A. Klümper, Nucl. Phys. B 546 751 (1999).
143. A. Klümper, Lect. Notes Phys. 645 349 (2004).
144. A. Kuniba, T. Nakanishi and J. Suzuki, Int. J. Mod. Phys. A 9 5215 (1994).
145. A. Kuniba, T. Nakanishi and J. Suzuki, Int. J. Mod. Phys. A 9 5267 (1994).
146. A.N. Kirillov and N.Yu. Reshetikhin, J. Phys. A 20 1565 (1987).
147. Z. Tsuboi, J. Phys. A 37 1747 (2004).
148. Z. Tsuboi and M. Takahashi, J. Phys. Soc. Japan 74 898 (2005).
149. Z. Tsuboi, Nucl. Phys. B 737 261 (2006).
150. M.T. Batchelor, X.-W. Guan, N. Oelkers and Z.-J. Ying, J. Stat. Phys. 116 571 (2004).
151. Z.-J. Ying, I. Roditi, A. Foerster and B. Chen, Eur. Phys. J. B 41 67 (2004).
152. Z.-J. Ying, I. Roditi and H.-Q. Zhou, arXiv:cond-mat/0405274 (2004).
153. M.T. Batchelor, X.-W. Guan and N. Oelkers, Phys. Rev. B 70 184408 (2004).
154. M.T. Batchelor, X.-W. Guan, N. Oelkers and Av. Foerster, J. Stat. Mech. P10017 (2004).
155. A. Feher, M. Orendáč, A. Orendáčová and E. Čižmár, Low Temp. Phys. 28 551 (2002).
156. M. Orendáč, A. Orendáčová, J. Cernák, A. Feher, P.J.C. Signore, M.W. Meisel, S. Merah and M. Verdaguer, Phys. Rev. B 52 3435 (1995).
157. Z.-J. Ying, A. Foerster, X.-W. Guan, B. Chen and I. Roditi, Eur. Phys. J. B 38 535 (2004).
158. Z.-J. Ying, X.-W. Guan, A. Foerster, I. Roditi and B. Chen, arXiv:cond-mat/0309718 (2003).
159. K. Katoh, Y. Hosokoshi and K. Inoue, J. Phys. Soc. Japan 69 1008 (2000).
160. Y. Hosokoshi, K. Katoh, A.S. Markosyan and K. Inoue, Synthetic Metals 121 1838 (2001).
161. Z. Honda, Y. Nonomura and K. Katsumata, J. Phys. Soc. Japan 66 3689 (1997).
162. W. Zheng, R.R.P. Singh and J. Oitmaa, Phys. Rev. B 55 8052 (1997).
163. X. Wang and L. Yu, Phys. Rev. Lett. 84 5399 (2000).
164. M. Hagiwara, H.A. Katori, U. Schollwöck and H.-J. Mikeska, Phys. Rev. B 62 1051 (2000).
165. M.J. Bhaseen and A.M. Tsvelik, Phys. Rev. B 68 094405 (2003).
166. D. Senechal, Phys. Rev. B 52 15319 (1995).
167. G. Sierra, J. Math. Phys. 29 3299 (1996).
168. G. Sierra, Lecture Notes in Physics 478 137 (1997).
169. I. Affleck, J. Phys. Condens. Matter. 1 3047 (1989).
170. Y.Q. Li, M. Ma, D.N. Shi and F.C. Zhang, Phys. Rev. Lett. 81 3527 (1998).
171. S.J. Gu and Y.Q. Li, Phys. Rev. B 66 092404 (2002).
172. S.J. Gu, Y.Q. Li and H.-Q Zhou, Phys. Rev. B 69 144405 (2004).
173. H.M. Babujian, Nucl. Phys. B 215 317 (1983).
174. A.N. Kirillov J. Sov. Math. 36 115 (1987).
175. B.W. Roos, Analytic Functions and Distributions in Physics and Engineering, (John Wiley & Sons, London, 1969).
176. A. Klümper, T. Wehner and J. Zittartz, J. Phys. A 30 1897 (1997).
177. P.P. Kulish, N.Yu. Reshetikhin and E.K. Sklyanin, Lett. Math. Phys. 5 393 (1981).
178. V.V. Bazhanov and N. Reshetikhin, J. Phys. A 23 1477 (1990).
179. M. Takahashi, in Physics and Combinatorics, edited by A.N. Kirillov and N. Liskova (World Scientific, Singapore, 2001), p. 299.
180. M. Takahashi, M. Shiroishi and A. Klümper, J. Phys. A 34 L187 (2001).
181. G. Kato and M. Wadati, J. Math. Phys. 43 5060 (2002).
182. A.N. Kirillov, J. Sov. Math. 47 2450 (1989).
183. A.N. Kirillov and N.Yu. Reshetikhin, J. Sov. Math. 52 3156 (1990).
184. N. Elstner and R.R.P. Singh, Phys. Rev. B 58 11484 (1998).
185. S. Miyahara and K. Ueda, J. Phys. Condens. Matter 15 R327 (2003).
186. S. Capponi and D. Poilblanc, Cond-mat/0612162 (2006).
187. B. Chiari, O. Piovesana, T. Tarantelli and P.F. Zanazzi, Inorg. Chem. 29 1172 (1990).
188. H. Mayaffre, M. Hovatiá, C. Berthier, M.-H. Julien, P. Ségransan, L. Lévy and O. Piovesana, Phys. Rev. Lett. 85 4795 (2000).
189. M.B. Stone, Y. Chen, J. Rittner, H. Yardimci, D.H. Reich, C. Broholm, D.V. Ferraris and T. Lectka, Phys. Rev. B 65 064423 (2002).
190. D.N. Aristov and M.N. Kiselev, Phys. Rev. B 70 224402 (2004).
191. S. Chen, L. Wang and Y. Wang, arXiv:cond-mat/0609269 (2006).
192. S. Miyahara, F. Becca and F. Mila, Phys. Rev. B 68 024401 (2003).
193. T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi and Y. Hosokoshi, K. Kato, K. Inoue and T. Goto, Phys. Stat. Sol. b 236 429 (2003).
194. M. Hagiwara, Y. Narumi, K. Kindo, M. Kohno, H. Nakano, R. Sato and M. Takahashi, RIKEN Review 46 14 (2002).
195. T. Sakai, K. Okamoto, K. Okunishi, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Katoh, K. Inoue and T. Goto, Physica B 346-347 34 (2004).
196. W. Bao, C. Broholm, G. Aeppli, P. Dai, J. M. Honig and P. Metcalf, Phys. Rev. Lett. 78 507 (1997).
197. Y. Tokura and N. Nagaosa, Science 288 462 (2000).
198. G. Khaliullin and S. Maekawa, Phys. Rev. Lett. 85 3950 (2000).
199. M. Mochizuki and M. Imada, Phys. Rev. Lett. 91 167203 (2003).
200. G. Khaliullin, P. Horsch and A.M. Oleś, Phys. Rev. Lett. 86 3879 (2001).
201. Y. Yamashita, N. Shibata and K. Ueda, Phys. Rev. B 61 4012 (2000).
202. Y. Yamashita, N. Shibata and K. Ueda, Phys. Rev. B 58 9114 (1998).
203. K. Penc, M. Mambrini, P. Fazekas and F. Mila, Phys. Rev. B 68 012408 (2003).
204. M. van den Bossche, P. Azaria, P. Lecheminant and F. Mila, Phys. Rev. Lett. 86 4124 (2001).
205. C. Itoi, S. Qin and I. Affleck, Phys. Rev. B 61 6747 (2000).
206. J. Sirker, Phys. Rev. B 69 104428 (2004).
207. B. Frischmuth, F. Mila and M. Troyer, Phys. Rev. Lett. 82 835 (1999).
208. A. Kawaguchi and N. Kawakami, J. Phys. Soc. Jpn. 71 3096 (2002).
209. M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78 1984 (1997).
210. B. Sutherland, Phys. Rev. B 62 11499 (2000).
211. M. Sato, Phys. Rev. B 71 024402 (2005).
212. Y. Hosokoshi, K. Katoh, A.S. Markosyan and K. Inoue, Sythetic Matals 121 1838 (2001).
213. T. Sakai, N. Okazaki, K. Okamoto, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Kato, K. Inoue and T. Goto, Phys. Stat. Sol. b 236 429 (2003).
214. H. Ohta, K. Kirita, T. Kunimoto, S. Okubo, Y. Hosokoshi, K. Katoh, K. Inoue, A. Ogasahara and S. Miyashita, J. Phys. Soc. Jpn. 71 2640 (2002).
215. T. Sakai, K. Okamoto, K. Okunishi, K. Kindo, Y. Narumi, Y. Hosokoshi, K. Katoh, K. Inoue and T. Goto, Physica B, 346-347 34 (2004).
216. J. Damerau and A. Klümper, J. Stat. Mech. P014. (2006).
217. F. Göhmann, A. Klümper and A. Seel, J. Phys. A 38 1833 (2005).
218. F. Göhmann, A. Klümper and A. Seel, J. Phys. A 37 7625 (2004).
219. F. Göhmann, A. Klümper and A. Seel, Physica B 359 807 (2005).
220. F. Göhmann, A. Seel, Theor. Math. Phys. 146 119 (2006).
221. F. Göhmann, N.P. Hasenclever, A. Seel, J. Stat. Mech. P015 (2005).
222. H.E. Boos, F. Göhmann, A. Klümper, J. Suzuki, J. Stat. Mech. P001 (2006).
223. Z. Tsuboi and M. Shiroishi, J. Phys. A 38 L363 (2005).
224. Z. Tsuboi, Physica A 377 95 (2007).
225. N. Fukushima, Y. Kuramoto, J. Phys. Soc. Jpn. 71 1238 (2002).
226. N. Fukushima, J. Stat. Phys. 111 1049 (2003).
227. I. Bloch, Nature Physics 1 23 (2005).
228. A. Micheli, G.K. Brennen and P. Zoller, Nature Physics 2 341 (2006).
229. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen De and U. Sen, Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond, Adv. Phys. 56 243 (2007).
230. S. Fujimoto and S. Eggert, Phys. Rev. Lett. 92 037206 (2004).