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Quantum breathers in a finite Heisenberg spin chain with antisymmetric interactions

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Abstract

A study of the likelihood of quantum breathers in a quantum Heisenberg spin system including a Dzyaloshinsky-Moriya interaction (DMI) is done through an extended Bose-Hubbard model while using the scheme of few body physics. The energy spectrum of the resulting Bose-Hubbard Hamiltonian, on a periodic one-dimensional lattice containing more than two quanta shows interesting detailed band structures. From a non degenerate, and a degenerate perturbation theory in addition to a numerical diagonalization, a careful investigation of these fine structures is set up. The attention is focussed on the effects of various interactions that are; the DMI, the Heisenberg in-plane (X, Y) as well as the out of plane exchange interaction on the energy spectrum of such a system. The outcome displays a possibility of an energy self-compensation in the system. We also computed the weight function of the eigenstates in direct space and in the space of normal modes. From a perturbation theory it is shown that the interaction between the quanta leads to an algebraic localization of the modified extended states in the normal-mode space of the non-interacting system that are coined quantum q-breathers excitations.

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References

  1. J.C. Eilbeck, in Localization and Energy Transfer in Nonlinear Systems, edited by L. Vazquez, R.S. Mackay, M.P. Zorzano (Word Scientific, Singapore, 2003), p. 177

  2. S. Flach, C.R. Willis, Phys. Rep. 295, 181 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  3. S. Flach, R.S. Mackay, Physica D 119, special volume (1999)

  4. J. Dorignac, J.C. Eilbeck, Phys. Rev. Lett. 93, 025504 (2004)

    Article  ADS  Google Scholar 

  5. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

  6. T. Moriya, Phys. Rev. Lett. 4, 228 (1960)

    Article  ADS  Google Scholar 

  7. T. Moriya, Phys. Rev. 120, 91 (1960)

    Article  ADS  Google Scholar 

  8. M. Elhajal, Lows energies properties and anisotropies of interactions of geometricaly frustrated magnetics systems, thesis, University Joseph Fourier Grenoble 1, 2002

  9. J. Sznajd, Phys. Rev. B 68, 174420 (2003)

    Article  ADS  Google Scholar 

  10. C. Ederer, N.A. Spaldin, Phys. Rev. B 71, 060401 (2005)

    Article  ADS  Google Scholar 

  11. R. Ballou, B. Canals, M. Elhajal, C. Lacroix, A.S. Wills, Phys. Stat. Sol. B 236, 240 (2003)

    Article  ADS  Google Scholar 

  12. A. Antal et al., Phys. Rev. B 77, 174429 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  13. E.Y. Vedmedenko, L. Udvardi, P. Weinberges, R. Wiesendager, Phys. Rev. B 75, 104431 (2007)

    Article  ADS  Google Scholar 

  14. Olivier Cepas, T. Ziman (2002), arXiv:Cond-mat/ 0207116v1

  15. A.L. Chenyshev, Phys. Rev. B 72, 174414 (2005)

    Article  ADS  Google Scholar 

  16. I.A. Segienko, E. Dagotto, Phys. Rev. B 73, 094434 (2006)

    Article  ADS  Google Scholar 

  17. M. Oshikawa, I. Affleck, Phys. Rev. Lett, 79, 2883 (1997)

    Article  ADS  Google Scholar 

  18. I. Affleck, M. Oshikawa, Phys. Rev. B 60, 1038 (1999)

    Article  ADS  Google Scholar 

  19. S. Miyashita, S. Tanaka, H. De Raedt, B. Barbara (2009), arXiv:Cond-mat. Stat. mech/080815 v4

  20. A. Zorko et al., Phys. Rev. Lett. 101, 026405 (2008)

    Article  ADS  Google Scholar 

  21. G.A. Jorge et al., Phys. Rev. B 71, 092403 (2005)

    Article  ADS  Google Scholar 

  22. O. Ofer, The Impact of Perturbation on Frusted Magnets, Institute of Technology, thesis, 2008

  23. R.A. Pinto, S. Flach, Phys. Rev. B 79, 66002 (2007)

    MathSciNet  Google Scholar 

  24. J. Elder, P. Hamm, A.C. Scott, Phys. Rev. Lett. 88, 067403 (2002)

    Article  ADS  Google Scholar 

  25. A. Xie, L. Van der Meer, W. Hoff, R.H. Austin, Phys. Rev. Lett. 84, 5435 (2000)

    Article  ADS  Google Scholar 

  26. G.L. Alfimov, V.V. Konotop, M. Salerno, Europhys. Lett. 58, 7 (2002)

    Article  ADS  Google Scholar 

  27. R. Carretero-Gonzalez, K. Promislow, Physica A 66, 033610 (2002)

    Article  Google Scholar 

  28. R. Lai, S.A. Kiselev, A.J. Sievers, Phys. Rev. B 56, 5345 (1999)

    Article  ADS  Google Scholar 

  29. G.P. Tsironis, Chaos 13, 657 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. J.P. Nguenang, R.A. Pinto, S. Flach, Phys. Rev. B 75, 214303 (2007)

    Article  ADS  Google Scholar 

  31. R.A. Pinto, J.P. Nguenang, S. Flach, Physica D 238, 581 (2009)

    Article  ADS  MATH  Google Scholar 

  32. Hu Xin-Guang, Tang Yi Chin, Phys. Soc. 17, 4268 (2008)

    Google Scholar 

  33. A.C. Scott, J.C. Eilbeck, H. Gilhoj, Physica D 78, 194 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. A.C. Scott, Nonlinear Science, 2nd edn. (Oxford University, New York, 2003)

  35. J.C. Eilbeck, F. Palmero, Quatum breathers in an attractive fermionic Hubbard model, in Nonlinear Waves: Classical a Quantum Aspects, edited by F.Kh. Abdullaev, V.V. Konotop (Kluwer, Amsterdam, 2004), p. 399

  36. L. Proville, Phys. Rev. B 71, 104306 (2005)

    Article  ADS  Google Scholar 

  37. L. Proville, Phys. Rev. B 72, 184301 (2005)

    Article  ADS  Google Scholar 

  38. J.C. Eilbeck, F. Palmero, Phys. Lett. A 331, 201, (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. V. Pouthier, C. Falvo, Phys. Rev. E 69, 041906 (2004)

    Article  ADS  Google Scholar 

  40. C. Falvo, V. Pouthier, J. Chem. Phys. 123, 184710 (2005)

    Article  ADS  Google Scholar 

  41. J.C. Eilbeck, Proceedings of the third Conference: Localization and energy transfer in nonlinear systems (2003), p. 177

  42. L.J. Bernstein, Physica D 68, 174 (1993)

    Article  ADS  MATH  Google Scholar 

  43. L. Bernstein, J.C. Eilbeck, A.C. Scott, Nonlinearity 3, 293 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. S. Aubry, S. Flach, K. Kladko, E. Olbrich, Phys. Rev. Lett. 76, 1607 (1996)

    Article  ADS  Google Scholar 

  45. S. Aubry, Physica D 103, 201 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. J.M. Radcliffe, J. Phys. A 4, 313 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  47. R. Bolakrishman, A.R. Bishop, Phys. Rev. Lett. 55, 537 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  48. J.P. Nguenang, M. Peyrard, A.J. Kenfack, T.C. Kofane, J. Phys.: Condens. Matter 17, 3083 (2005)

    Article  ADS  Google Scholar 

  49. Z.I. Djoufack, A. Kenfack-Jiotsa, J.-P. Nguenang, S. Domngang, J. Phys.: Condens. Matter 22, 205502 (2010)

    Article  ADS  Google Scholar 

  50. B. Gölzer, A. Holz, J. Phys. A 20, 3327 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  51. T. Holstein, H. Primakoff, Phys. Rev. 58, 1098 (1940)

    Article  ADS  MATH  Google Scholar 

  52. J.C. Eilbeck, H. Gilhoj, A.C. Scott, Phys. Lett. A 172, 229 (1993)

    Article  ADS  Google Scholar 

  53. W.H. Press, S.A. Teukolsky, W.T. Vetterding, B.P. Flannery, Numerical Recipes in Fortran 77 the Art of Scientific Computing, 2nd edn. (Cambridge University Press, 1986, 1992)

  54. C. Falvo, V. Pouthier, Chem. Phys. 123, 184709 (2005)

    ADS  Google Scholar 

  55. M. Valiente, D. Petrosyan, J. Phys. B At. Mol. Opt. Phys. 41, 161002 (2008)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Nonlinear Physics and Complex Systems Group, Département de Physique, École Normale Supérieure, Universitéde Yaoundé I, B.P. 47, Yaoundé, Cameroon

    Z. I. Djoufack & A. Kenfack-Jiotsa

  2. Materials Sciences Laboratory, Department of Physics, Faculty of Sciences, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

    Z. I. Djoufack

  3. A.S. International Centre for Theoretical Physics, Strada Costiera 11, Trieste, Italy

    A. Kenfack-Jiotsa & J. P. Nguenang

  4. Fundamental Physics Laboratory. Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of Sciences, University of Douala, P.O. Box 24157, Douala, Cameroon

    J. P. Nguenang

Authors
  1. Z. I. Djoufack
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  2. A. Kenfack-Jiotsa
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  3. J. P. Nguenang
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Correspondence to J. P. Nguenang.

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Djoufack, Z.I., Kenfack-Jiotsa, A. & Nguenang, J.P. Quantum breathers in a finite Heisenberg spin chain with antisymmetric interactions. Eur. Phys. J. B 85, 96 (2012). https://doi.org/10.1140/epjb/e2012-20707-1

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