Quantum criticality in dimerized spin ladders

Physical Review B - Condensed Matter and Materials Physics

Volumn 77, Issue 22, 2008, Pages

  Chitov, Gennady Y ^a   Ramakko, Brandon W ^a   Azzouz, Mohamed ^a,b  

^a LAURENTIAN UNIVERSITY   (Canada)

^b AL AKHAWAYN UNIVERSITY   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 45749116907     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.224433     Document Type: Article

References (30)

1. E. Dagotto and T. M. Rice, Science SCIEAS 0036-8075 10.1126/science.274. 5287.618 271, 618 (1996).
2. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).
3. P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.17 78, 17 (2006).
4. M. A. Martin-Delgado, R. Shankar, and G. Sierra, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3443 77, 3443 (1996).
5. M. A. Martin-Delgado, J. Dukelsky, and G. Sierra, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00849-4 250, 430 (1998).
6. V. N. Kotov, J. Oitmaa, and Zheng Weihong, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.11377 59, 11377 (1999).
7. D. C. Cabra and M. D. Grynberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1768 82, 1768 (1999).
8. Y.-J. Wang and A. A. Nersesyan, Nucl. Phys. B: Field Theory Stat. Syst. NBSSDR 0169-6823 583, 671 (2000).
9. K. Okamoto, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.212408 67, 212408 (2003).
10. M. Nakamura, T. Yamamoto, and K. Ide, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.72.1022 72, 1022 (2003).
11. J. Almeida, M. A. Martin-Delgado, and G. Sierra, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.184428 76, 184428 (2007).
12. J. Almeida, M. A. Martin-Delgado, and G. Sierra, arXiv:0707.4452 (unpublished).
13. In this work we study the case of the antiferromagnetic (positive) spin exchange couplings only.
14. M. Azzouz, K. Shahin, and G. Y. Chitov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.76.132410 76, 132410 (2007)
15. K. Shahin, M.S. thesis, Laurentian University, 2007.
16. M. Azzouz, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.6136 48, 6136 (1993).
17. M. Azzouz, L. Chen, and S. Moukouri, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.6233 50, 6233 (1994).
18. M. Azzouz and K. A. Asante, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.094433 72, 094433 (2005).
19. See, e.g., E. Chattopadhyay and I. Bose, Physica A PHYADX 0378-4371 10.1016/S0378-4371(02)01396-1 318, 14 (2003).
20. J. L. Black and V. J. Emery, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.23.429 23, 429 (1981).
21. 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).
22. T. Papenbrock, T. Barnes, D. J. Dean, M. V. Stoitsov, and M. R. Strayer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.024416 68, 024416 (2003).
23. E. Orignac, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00198-5 39, 335 (2004)
24. E. Orignac and R. Chitra, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.214436 70, 214436 (2004).
25. Note that contrary to the sine-Gordon formula 11, the logarithmically corrected dimerized chain energy 10 is lower than the plaquette energy 9 in the region δeff 0.4. However, formulas 10 9 are reliable only when δeff 1.
26. The other band E2s can be excluded from further considerations since it has a bigger nonvanishing gap.
27. G. Y. Chitov and C. Gros, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.104423 69, 104423 (2004).
28. L. N. Bulaevskii, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 44, 1008 (1963)
29. L. N. Bulaevskii, [Sov. Phys. JETP SPHJAR 0038-5646 17, 684 (1963)].
30. Using the formula for the NLσM topological term derived in Ref., we obtain the critical line located between two points: (δ= 18 35 =0.5142..., J=0) and (δ=1, J/J=1.9823...). So this approach does not result in adequate predictions.