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Quantum spin chains: Simple models with complex dynamics

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The present study highlights some of the complexities observed in the dynamical properties of one-dimensional quantum spin systems. Exact results for zero-temperature dynamic correlation functions are presented for two contrasting situations:

  1. (i)

    a system with a fully ordered ferromagnetic ground state;

  2. (ii)

    a system at aT c=0 critical point.

For both situations it is found that the exact results are considerably more complex than has been anticipated on the basis of approximate approaches which are considered to be appropriate and reliable for such situations. A still higher degree of complexity is expected for the dynamics of quantum spin systems which are nonintegrable. The paper concludes with some observations concerning nonintegrability effects and quantum chaos in spin systems.

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References

  1. Haldane, F.D.M.: Phys. Lett.93A, 464 (1983); Phys. Rev. Lett.50, 1153 (1983); (unpublished)

    Google Scholar 

  2. Steiner, M., Villain, J., Windsor, C.G.: Adv. Phys.25, 87 (1976)

    Google Scholar 

  3. Magnetostructural correlations in exchange coupled systems. Willett, R.D., Gatteschi, D., Kahn, O. (eds.). Boston: D. Reidel Publishing Co. 1985

    Google Scholar 

  4. Groen, J.P., Klaassen, T.O., Poulis, N.J., Müller, G., Thomas, H., Beck, H.: Phys. Rev. B22, 5369 (1980)

    Google Scholar 

  5. Anderson, P.W.: Science235, 1196 (1987)

    Google Scholar 

  6. More precisely: normal modes of the classical equations of motion linearized about the exact classical ground state

  7. Luther, A., Peschel, I.: Phys. Rev. B12, 3908 (1975)

    Google Scholar 

  8. Müller, G., Thomas, H., Beck, H., Bonner, J.C.: Phys. Rev. B24, 1429 (1981)

    Google Scholar 

  9. Müller, G., Thomas, H., Puga, M.W., Beck, H.: J. Phys. C14, 3399 (1981)

    Google Scholar 

  10. Müller, G.: Phys. Rev. B26, 1311 (1982)

    Google Scholar 

  11. Kurmann, J., Thomas, H., Müller, G.: Physica112A, 235 (1982)

    Google Scholar 

  12. Taylor, J.H., Müller, G.: Phys. Rev. B28, 1529 (1983)

    Google Scholar 

  13. Müller, G., Shrock, R.E.: Phys. Rev. B32, 5845 (1985)

    Google Scholar 

  14. Barouch, E., McCoy, B.M.: Phys. Rev. A3, 786 (1971)

    Google Scholar 

  15. Suzuki, M.: Prog. Theor. Phys.46, 1337 (1971)

    Google Scholar 

  16. Yang, C.N.: Phys. Rev.85, 808 (1952)

    Google Scholar 

  17. Lieb, E., Schultz, T., Mattis, D.: Ann. Phys. (NY)16 407 (1961)

    Google Scholar 

  18. Katsura, S.: Phys. Rev.127, 1508 (1962)

    Google Scholar 

  19. Niemeijer, T.: Physica36, 377 (1967)

    Google Scholar 

  20. Katsura, S., Horiguchi, T., Suzuki, M.: Physica46, 67 (1970)

    Google Scholar 

  21. McCoy, B.M., Barouch, E., Abraham, D.B.: Phys. Rev. A4, 2331 (1971)

    Google Scholar 

  22. McCoy, B.M., Perk, J.H.H., Shrock, R.E.: Nucl. Phys. B220 [FS8], 35 (1983); B220 [FS8], 269 (1983)

    Google Scholar 

  23. Müller, G., Shrock, R.E.: Phys. Rev. B29, 288 (1984); J. Appl. Phys.55, 1874 (1984)

    Google Scholar 

  24. Lichtenberg, A.J., Lieberman, M.A.: Regular and stochastic motion. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  25. Müller, G.: Phys. Rev. A34, 3345 (1986)

    Google Scholar 

  26. Magyari, E., Thomas, H., Weber, R., Kaufman, C., Müller, G.: Z. Phys. B-Condensed Matter65, 363 (1987); Srivastava, N., Kaufman, C., Müller, G., Magyari, E., Weber, R., Thomas, H.: J. Appl. Phys.61, 4438 (1987)

    Google Scholar 

  27. Zaslavsky, G.M.: Chaos in dynamic systems. New York: Harwood, 1985

    Google Scholar 

  28. Müller, G., Shrock, R.E.: Phys. Rev. B30, 5254 (1984); B31, 637 (1985)

    Google Scholar 

  29. Duxbury, P.M., Oitmaa, J., Barber, M.N., Bilt, A. van der Joung, K.O., Carlin, R.L.: Phys. Rev. B24, 5149 (1981)

    Google Scholar 

  30. Bonner, J.C.: p. 157

    Google Scholar 

  31. Sutherland, B.: Phys. Rev. B12, 3795 (1975); Takhtajan, L.A.: Phys. Lett.87A, 479 (1982); Babujian, H.M.: ibid.90A, 479 (1982)

    Google Scholar 

  32. Affleck, I.: Nucl. Phys. B265 [FS 15], 409 (1986)

    Google Scholar 

  33. Oitmaa, J., Parkinson, J.B., Bonner, J.C.: J. Phys. C19, L595 (1986)

    Google Scholar 

  34. Blöte, H.W.J., Capel, H.: Physica A (in press)

  35. Bonner, J.C., Parkinson, J.B., Oitmaa, J., Blöte, H.W.J.: J. Appl. Phys.61, 4432 (1987)

    Google Scholar 

  36. Müller, G., Bonner, J.C., Parkinson, J.B.: J. Appl. Phys.61, 3950 (1987)

    Google Scholar 

  37. Nightingale, M.P., Blöte, H.W.J.: Phys. Rev. B33, 659 (1986)

    Google Scholar 

  38. Bonner, J.C., Parkinson, J.B.: J. Phys. C (submitted for publication)

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Authors and Affiliations

  1. Department of Physics, The University of Rhode Island, 02881, Kingston, Rhode Island, USA

    G. Müller

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  1. G. Müller
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Dedicated to Professor Harry Thomas on the occasion of his 60th birthday

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Müller, G. Quantum spin chains: Simple models with complex dynamics. Z. Physik B - Condensed Matter 68, 149–159 (1987). https://doi.org/10.1007/BF01304220

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  • DOI: https://doi.org/10.1007/BF01304220

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