Statics and dynamics of weakly coupled antiferromagnetic spin-12 ladders in a magnetic field

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 5, 2011, Pages

  Bouillot, Pierre ^a   Kollath, Corinna ^a,b   Läuchli, Andreas M ^c   Zvonarev, Mikhail ^d,e   Thielemann, Benedikt ^f   Rüegg, Christian ^g   Orignac, Edmond ^h   Citro, Roberta ⁱ   Klanjšek, Martin ^j,k   Berthier, Claude ^k   Horvatić, Mladen ^k   Giamarchi, Thierry ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^d HARVARD UNIVERSITY   (United States)

^e UNIVERSITÉ PARIS SUD   (France)

^f Laboratory for Neutron Scattering Villigen   (Switzerland)

^g UNIVERSITY COLLEGE LONDON   (United Kingdom)

^h CNRS   (France)

ⁱ UNIVERSITY OF SALERNO   (Italy)

^j JO EF STEFAN INSTITUTE   (Slovenia)

^k IRISA   (France)

more..

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953232356     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.054407     Document Type: Article

References (106)

1. A. Auerbach, Interacting Electrons and Quantum Magnetism, 2nd ed. (Springer, Berlin, 1998).
2. T. Giamarchi and A. M. Tsvelik, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.59.11398 59, 11398 (1999).
3. T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5868 84, 5868 (2000).
4. C. Rüegg, N. Cavadini, A. Furrer, H.-U. Güdel, K. Krämer, H.Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Nature (London) NATUAS 0028-0836 10.1038/nature01617 423, 62 (2003). (Pubitemid 36575442)
5. T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Nat. Phys. NATUAS 1745-2473 10.1038/nphys893 4, 198 (2008).
6. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).
7. A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, UK, 1999).
8. E. Dagotto and T. M. Rice, Science SCIEAS 0036-8075 10.1126/science.271. 5249.618 271, 5249 (1996).
9. S. Gopalan, T. M. Rice, and M. Sigrist, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.49.8901 49, 8901 (1994).
10. Zheng Weihong, V. Kotov, and J. Oitmaa, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.57.11439 57, 11439 (1998).
11. M. Troyer, H. Tsunetsugu, and D. Würtz, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.50.13515 50, 13515 (1994).
12. T. Barnes, E. Dagotto, J. Riera, and E. S. Swanson, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.47.3196 47, 3196 (1993).
13. M. Reigrotzki, H. Tsunetsugu, and T. M. Rice, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/6/43/021 6, 9235 (1994).
14. W. Zheng, C. J. Hamer, R. R. P. Singh, S. Trebst, and H. Monien, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.63.144410 63, 144410 (2001).
15. O. P. Sushkov and V. N. Kotov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.1941 81, 1941 (1998).
16. C. Knetter, K. P. Schmidt, M. Grüninger, and G. S. Uhrig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.167204 87, 167204 (2001).
17. F. Mila, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050542 6, 201 (1998).
18. E. Orignac, R. Citro, and T. Giamarchi, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.75.140403 75, 140403 (R) (2007).
19. R. Chitra and T. Giamarchi, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.55.5816 55, 5816 (1997).
20. A. Furusaki and S. C. Zhang, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.60.1175 60, 1175 (1999).
21. X. Wang and L. Yu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 84.5399 84, 5399 (2000).
22. S. Wessel, M. Olshanii, and S. Haas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.206407 87, 206407 (2001).
23. B. Normand and C. Rüegg, e-print arXiv: 1006.4196 (2010).
24. Y. Maeda, C. Hotta, and M. Oshikawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.057205 99, 057205 (2007). (Pubitemid 47191902)
25. M. Usami and S.-i. Suga, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.58.14401 58, 14401 (1998).
26. T. Hikihara and A. Furusaki, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.63.134438 63, 134438 (2001).
27. M. Tachiki, T. Yamada, and S. Maekawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.29.663 29, 663 (1970).
28. B. R. Patyal, B. L. Scott, and R. D. Willett, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.41.1657 41, 1657 (1990).
29. C. Rüegg, K. Kiefer, B. Thielemann, D. F. McMorrow, V. Zapf, B.Normand, M. B. Zvonarev, P. Bouillot, C. Kollath, T. Giamarchi, S. Capponi, D. Poilblanc, D. Biner, and K. W. Krämer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.247202 101, 247202 (2008).
30. M. Klanjšek, H. Mayaffre, C. Berthier, M. Horvatić, B. Chiari, O. Piovesana, P. Bouillot, C. Kollath, E. Orignac, R. Citro, and T. Giamarchi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.137207 101, 137207 (2008).
31. B. Thielemann, C. Rüegg, K. Kiefer, H. M. Rønnow, B. Normand, P. Bouillot, C. Kollath, E. Orignac, R. Citro, T. Giamarchi, A. M. Läuchli, D. Biner, K. W. Krämer, F. Wolff-Fabris, V. S. Zapf, M. Jaime, J. Stahn, N. B. Christensen, B. Grenier, D. F. McMorrow, and J. Mesot, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.020408 79, 020408 (R) (2009).
32. B. Thielemann, C. Rüegg, H. M. Rønnow, A. M. Läuchli, J.-S. Caux, B. Normand, D. Biner, K. W. Krämer, H.-U. Güdel, J. Stahn, K. Habicht, K. Kiefer, M. Boehm, D. F. McMorrow, and J. Mesot, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.107204 102, 107204 (2009).
33. A. T. Savici, G. E. Granroth, C. L. Broholm, D. M. Pajerowski, C. M. Brown, D. R. Talham, M. W. Meisel, K. P. Schmidt, G. S. Uhrig, and S. E. Nagler, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.80.094411 80, 094411 (2009).
34. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
35. J.-S. Caux, R. Hagemans, and J.-M. Maillet, J. Stat. Mech.: Theor. Exp. RMPHAT 1742-5468 10.1088/1742-5468/2005/09/P09003 (2005) P09003.
36. J.-S. Caux, P. Calabrese, and N. A. Slavnov, J. Stat. Mech.: Theory Exp. RMPHAT 1742-5468 10.1088/1742-5468/2007/01/P01008 (2007) P01008.
37. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.040502 93, 040502 (2004).
38. S. R. White and A. E. Feiguin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.076401 93, 076401 (2004).
39. A. Daley, C. Kollath, U. Schollwöck, and G. Vidal, J. Stat. Mech.: Theory Exp. PRLTAO 1742-5468 10.1088/1742-5468/2004/04/P04005 (2004) P04005.
40. U. Schollwöck and S. R. White, in Effective Models for Low-Dimensional Strongly Correlated Systems, edited by, G. G. Batrouni, and, D. Poilblanc, (AIP, Melville, NY, 2006), p. 155.
41. F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207204 93, 207204 (2004).
42. M. Zwolak and G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207205 93, 207205 (2004).
43. A. E. Feiguin and S. R. White, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.72.220401 72, 220401 (2005). (Pubitemid 43022625)
44. H. J. Schulz, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.34.6372 34, 6372 (1986).
45. I. Affleck, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.41.6697 41, 6697 (1990).
46. S. Sachdev, T. Senthil, and R. Shankar, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.50.258 50, 258 (1994).
47. M. Tachiki and T. Yamada, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.28.1413 28, 1413 (1970).
48. G. Chaboussant, M.-H. Julien, Y. Fagot-Revurat, M. Hanson, L. Lévy, C. Berthier, M. Horvatic, and O. Piovesana, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050539 6, 167 (1998).
49. S. R. White, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.48.10345 48, 10345 (1993).
50. U. Schollwöck, Rev. Mod. Phys. 77 (2005).
51. K. A. Hallberg, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730600766432 55, 477 (2006). (Pubitemid 44773295)
52. E. Jeckelmann, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.176.143 176, 143 (2008).
53. M. Gaudin, La fonction d'onde de Bethe (Masson, Paris, 1983).
54. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, UK, 1993).
55. M. Takahashi and M. Suzuki, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.48.2187 48, 2187 (1972).
56. M. Takahashi, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.51.1348 51, 1348 (1974).
57. M. Takahashi, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.44.12382 44, 12382 (1991).
58. H. J. Schulz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77. 2790 77, 2790 (1996).
59. N. Nagaosa, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.39.2188 39, 2188 (1989).
60. S. Coleman, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.11.2088 11, 2088 (1975).
61. A. Luther, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.14.2153 14, 2153 (1976).
62. S. Lukyanov and A. B. Zamolodchikov, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(97)00123-5 493, 571 (1997).
63. O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.046701 66, 046701 (2002). (Pubitemid 40606337)
64. F. Alet, S. Wessel, and M. Troyer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.036706 71, 036706 (2005). (Pubitemid 40629742)
65. A. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. Manmana, M. Matsumoto, I. McCulloch, F. Michel, R. Noack, G. Pawlowski, L. Pollet, T. Pruschke, U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner, and S. Wessel, J. Magn. Magn. Mater. JMMMDC 0304-8853 10.1016/j.jmmm.2006.10.304 310, 1187 (2007).
66. The perturbative expression of the ground state in the spin liquid regime and the corresponding singlet and triplet densities are given in Appendix A.
67. An additional scaling factor 7.47 mJ/gK has to be applied on the theoretical specific heat (per rung) to convert to the experimental units.
68. S. Suga, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.77.074717 77, 074717 (2008).
69. C. P. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1980).
70. D. J. Scalapino, Y. Imry, and P. Pincus, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.11.2042 11, 2042 (1975).
71. C. Yasuda, S. Todo, K. Hukushima, F. Alet, M. Keller, M. Troyer, and H. Takayama, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.217201 94, 217201 (2005). (Pubitemid 41636699)
72. S. Todo and A. Shibasaki, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.224411 78, 224411 (2008).
73. G. Müller, H. Thomas, H. Beck, and J. C. Bonner, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.24.1429 24, 1429 (1981).
74. A. M. Läuchli, Manep Meeting, Les Diablerets (2007).
75. Note that the edge exponents in the incommensurate branches of the correlations (B5) are inverted compared to their expression in Ref. 20.
76. S. Sorella and A. Parola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4604 76, 4604 (1996).
77. S. Sorella and A. Parola, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.57.6444 57, 6444 (1998).
78. For the correlations S π zz and S 0 + -, some of these singularities correspond to the lower edge description in Ref. 20 and discussed in Sec. VC3a.
79. A. M. Läuchli and C. Rüegg (unpublished).
80. A. K. Kolezhuk and H.-J. Mikeska, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.65.014413 65, 014413 (2001).
81. A. K. Kolezhuk and H.-J. Mikeska, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.145.85 145, 85 (2002).
82. A. Friedrich, A. K. Kolezhuk, I. P. McCulloch, and U. Schollwöck, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.75.094414 75, 094414 (2007).
83. Note that in the strong coupling limit the energy scales set by J and h z become very close, such that this position is in agreement with the ones previously discussed for the strong coupling limit.
84. 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. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5168 86, 5168 (2001). (Pubitemid 32527765)
85. F. Anfuso, M. Garst, A. Rosch, O. Heyer, T. Lorenz, C. Rüegg, and K. Krämer, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.77.235113 77, 235113 (2008).
86. T. Lorenz, O. Heyer, M. Garst, F. Anfuso, A. Rosch, C. Rüegg, and K. Krämer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.067208 100, 067208 (2008). (Pubitemid 351391476)
87. E. Čižmár, M. Ozerov, J. Wosnitza, B. Thielemann, K. W. Krämer, C. Rüegg, O. Piovesana, M. Klanjšek, M. Horvatić, C. Berthier, and S. A. Zvyagin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.82.054431 82, 054431 (2010).
88. These parameters were the first outputs from the NMR measurements, which were later refined to the values from Ref. 30. Note that small changes in these values do not affect the main results of the calculations.
89. S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter (Oxford University Press, New York, 1986).
90. C. Rüegg, B. Normand, M. Matsumoto, C. Niedermayer, A. Furrer, K. W. Krämer, H.-U. Güdel, P. Bourges, Y. Sidis, and H. Mutka, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.267201 95, 267201 (2005). (Pubitemid 43065262)
91. S. Sachdev and R. N. Bhatt, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.41.9323 41, 9323 (1990).
92. J.-D. Picon, A. F. Albuquerque, K. P. Schmidt, N. Laflorencie, M. Troyer, and F. Mila, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.184418 78, 184418 (2008).
93. T. Hikihara and A. Furusaki, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.69.064427 69, 064427 (2004).
94. M. Klanjšek, H. Mayaffre, C. Berthier, M. Horvatić, B. Chiari, O. Piovesana, P. Bouillot, C. Kollath, E. Orignac, R. Citro, and T. Giamarchi, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/pssb.200983048 247, 656 (2010).
95. F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 45.1358 45, 1358 (1980).
96. M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.060406 79, 060406 (2009).
97. D. Gobert, C. Kollath, U. Schollwöck, and G. Schütz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.036102 71, 036102 (2005). (Pubitemid 40619782)
98. S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102. 190601 102, 190601 (2009).
99. E. Stoudenmire and S. R. White, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/5/055026 12, 055026 (2010).
100. n) only with its imaginary part that has no zero-frequency component as proposed in Ref. 106.
101. † = S β with α, β = z, +, -.
102. S. R. White and I. Affleck, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.77.134437 77, 134437 (2008).
103. T. Barthel, U. Schollwöck, and S. R. White, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.245101 79, 245101 (2009).
104. A. W. Sandvik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 5196 80, 5196 (1998).
105. O. Nohadani, S. Wessel, B. Normand, and S. Haas, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.69.220402 69, 220402 (2004).
106. R. G. Pereira, S. R. White, and I. Affleck, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.165113 79, 165113 (2009).