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Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder

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Abstract

The columnar dimerized antiferromagnetic S = 1/2 spin ladder is numerically studied by the density-matrix renormalization-group (DMRG) method. The elastic lattice with spin-phonon coupling α and lattice elastic force k is introduced into the system. Thus the S = 1 / 2 Heisenberg spin chain is unstable towards dimerization (the spin-Peierls transition). However, the dimerization should be suppressed if the rung coupling J ⊥ is sufficiently large, and a Columnar dimer to Rung singlet phase transition takes place. After a self-consistent calculation of the dimerization, we determine the quantum phase diagram by numerically computing the singlet-triplet gap, the dimerization amplitude, the order parameters, the rung spin correlation and quantum entropies. Our results show that the phase boundary between the Columnar dimer phase and Rung singlet phase is approximately of the form J ⊥ ~ \hbox{$(\frac{k}{\alpha^{2}})^{-\frac{5}{4}}$} ( k α 2 ) − 5 4.

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References

  1. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, Y. Kitaoka, Phys. Rev. Lett. 73, 3463 (1994)

    Article  ADS  Google Scholar 

  2. A.E. Feiguin, J.A. Riera, A. Dobry, H.A. Ceccatto, Phys. Rev. B 56, 14607 (1997)

    Article  ADS  Google Scholar 

  3. M. Hase, I. Terasaki, K. Uchinokura, Phys. Rev. Lett. 70, 3651 (1993)

    Article  ADS  Google Scholar 

  4. E. Orignac, R. Chitra, Phys. Rev. B 70, 214436 (2004)

    Article  ADS  Google Scholar 

  5. J.W. Bray, H.R. Hart Jr., L.V. Interrante, I.S. Jacobs, J.S. Kasper, G.D. Watkins, S.H. Wee, J.C. Bonner, Phys. Rev. Lett. 35, 744 (1975)

    Article  ADS  Google Scholar 

  6. I.S. Jacobs, J.W. Bray, H.R. Hart Jr., L.V. Interrante, J.S. Kasper, G.D. Watkins, D.E. Prober, J.C. Bonner, Phys. Rev. B 14, 3036 (1976)

    Article  ADS  Google Scholar 

  7. W.H. Zheng, V. Kotov, J. Oitmaa, Phys. Rev. B 57, 11439 (1998)

    Article  ADS  Google Scholar 

  8. O.A. Starykh, L. Balents, Phys. Rev. Lett. 93, 127202 (2004)

    Article  ADS  Google Scholar 

  9. G.H. Liu, H.L. Wang, G.S. Tian, Phys. Rev. B 77, 214418 (2008)

    Article  ADS  Google Scholar 

  10. M. Azzouz, K. Shahin, G.Y. Chitov, Phys. Rev. B 76, 132410 (2007)

    Article  ADS  Google Scholar 

  11. M.A. Martin-Delgado, R. Shankar, G. Sierra, Phys. Rev. Lett. 77, 3443 (1996)

    Article  ADS  Google Scholar 

  12. K. Okamoto, Phys. Rev. B 67, 212408 (2003)

    Article  ADS  Google Scholar 

  13. G.Y. Chitov, B.W. Ramakko, M. Azzouz, Phys. Rev. B 77, 224433 (2008)

    Article  ADS  Google Scholar 

  14. S.J. Gibson, R. Meyer, G.Y. Chitov, Phys. Rev. B 83, 104423 (2011)

    Article  ADS  Google Scholar 

  15. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)

    Article  ADS  Google Scholar 

  16. S.R. White, Phys. Rev. B 48, 10345 (1993)

    Article  ADS  Google Scholar 

  17. R. Bulla, T. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)

    Article  ADS  Google Scholar 

  18. S.J. Gu, S.S. Deng, Y.Q. Li, H.-Q. Lin, Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  19. J. Vidal, G. Palacios, R. Mosseri, Phys. Rev. A 69, 022107 (2004)

    Article  ADS  Google Scholar 

  20. J. Vidal, R. Mosseri, J. Dukelsky, Phys. Rev. A 69, 054101 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  21. M.F. Yang, Phys. Rev. A 71, 030302(R) (2005)

    ADS  Google Scholar 

  22. O. Legeza, J. Sólyom, Phys. Rev. Lett. 96, 116401 (2006)

    Article  ADS  Google Scholar 

  23. O. Legeza, J. Sólyom, L. Tincani, R.M. Noack, Phys. Rev. Lett. 99, 087203 (2007)

    Article  ADS  Google Scholar 

  24. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  25. L.A. Wu, M.S. Sarandy, D.A. Lidar, Phys. Rev. Lett. 93, 250404 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  26. R.A. Molina, P. Schmitteckert, Phys. Rev. B 75, 235104 (2007)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Key Laboratory for Advanced Microstructure Materials of the Ministry of Education and Department of Physics, Tongji University, Shanghai, 200092, P.R. China

    Y.J. Xu, H. Zhao & Y.G. Chen

  2. Department of Physics, Shaoxing University, Shaoxing, 312000, P.R. China

    Y.H. Yan

Authors
  1. Y.J. Xu
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  2. H. Zhao
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  3. Y.G. Chen
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  4. Y.H. Yan
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Correspondence to H. Zhao.

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Xu, Y., Zhao, H., Chen, Y. et al. Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder. Eur. Phys. J. B 85, 393 (2012). https://doi.org/10.1140/epjb/e2012-30316-7

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