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Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

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Zeitschrift für Physik B Condensed Matter

Abstract

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La2CuO4. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.

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References

  1. Bednorz, J.G., Müller, K.A.: Z. Phys. B-condensed Matter64, 189 (1986)

    Google Scholar 

  2. Wu, M.K., Ashburn, J.R., Torng, C.J., Hor, P.H., Meng, R.L., Gao, L., Huang, Z.J., Wang, Y.Q., Chu, C.W.: Phys. Rev. Lett.58, 908, (1987)

    Google Scholar 

  3. Fulde, P.: Physica C (in press)

  4. Rice, T.M.: Z. Phys. B-Condensed Matter67, 141 (1987)

    Google Scholar 

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

    Google Scholar 

  6. Anderson, P.W.: In: Proceedings of the International School of Physics “Enrico Fermi”, July 1987. Frontieres and borderlines in many particle physics. Amsterdam: North Holland (in press)

  7. Endoh, Y., Yamada, K., Birgeneau, R.J., Gabbe, D.R., Jenssen H.P., Kastner, M.A., Peters, C.J., Picone, P.J., Thurston, T.R. Tranquada, J.M, Shirane, G.: (Preprint)

  8. Emery, V.J.: Phys. Rev. Lett.58, 2794 (1987)

    Google Scholar 

  9. Weber, W.: (Preprint)

  10. Brinkmann, W.F., Rice, T.M.: Phys. Rev. B2, 796 (1970)

    Google Scholar 

  11. Klein, D.L., Seitz, W.A.: Phys. Re. B10, 3217 (1974). Chao K.A., Spalek, J., Oles, A.M.: J. Phys. C10, L271 (1977). Hirsch, J.E.: Phys. Rev. Lett.54, 1317 (1985)

    Google Scholar 

  12. Zhang, F.C., Rice, T.M.: Phys. Rev. B37, 3759 (1988)

    Google Scholar 

  13. Shirane, G., Endoh, Y., Birgeneau, R.J., Kastner, M.A., Hidaka, Y., Oda, M., Suzuki, M., Murakami, T.: Phys. Rev. Lett.59, 1613 (1987)

    Google Scholar 

  14. Tranquada, J.M. et al.: Phys. Rev. Lett.60, 156 (1988)

    Google Scholar 

  15. Bethe, H.: Z. Phys.71, 205 (1931)

    Google Scholar 

  16. Hulthen, J.L.: Ark. Mat. Astr. Fjs.26A, 1 (1938)

    Google Scholar 

  17. Lieb, E.H., Wu, F.Y.: Phys. Rev. Lett.20, 1445 (1968)

    Google Scholar 

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

    Google Scholar 

  19. Haldane, F.D.M.: Phys. Rev. Lett.60, 635 (1988) and ibid Phys. Rev. Lett.45, 1358 (1980)

    Google Scholar 

  20. Kaplan, T.A., Horsch, P., Borysowicz, J.: Phys. Rev. B35, 1877 (1987)

    Google Scholar 

  21. Neves, E.J., Perez, J.F.: Phys. Lett.114A, 331 (1986)

    Google Scholar 

  22. Oitmaa, J, Betts, D.D.: Can. J. Phys.56, 897 (1978). Betts, D. D., Oitmaa, J.: Phys. Lett. A62, 277 (1977)

    Google Scholar 

  23. Baskaran, G., Zou, Z., Anderson, P.W.: Solid State Commun.63, 973 (1987)

    Google Scholar 

  24. Ruckenstein, A.E., Hirschfeld, P.J., Appel, J.: Phys. Rev. B36, 857 (1987)

    Google Scholar 

  25. Müller-Hartmann, E., Drzaga, M., Kampf, A., Wischmann H.A.: (Preprint)

  26. Hirsch, J.E.: Phys. Rev. B31, 4403 (1985)

    Google Scholar 

  27. Petrasken, M.I., Trifonov, E.D.: Application of group theory in quantum mechanics (see Young-Tableaux). Cambridge, Mass: M.I.T. Press 1969

    Google Scholar 

  28. Gutzwiller, M.C.: Phys. Rev. Lett.10, 159 (1963), and Phys. Rev.134, A 923 (1964)

    Google Scholar 

  29. Kaplan, T.A., Horsch, P., Fulde, P.: Phys. Rev. Lett.49, 889 (1982)

    Google Scholar 

  30. Horsch, P., Kaplan, T.A.: J. Phys. C16, L1203 (1983)

    Google Scholar 

  31. Metzner, W., Wollhardt, D.: Phys. Rev. Lett.59, 121 (1987); Gebhard, F., Vollhardt, D.: ibid. Phys. Rev. Lett.59, 1472 (1987)

    Google Scholar 

  32. Horsch, P., Kaplan, T.A.: Bull. Am. Phys. Soc.30, 513 (1985) (and unpublished)

    Google Scholar 

  33. Gros, C., Joynt, R., Rice, T.M.: Phys. Rev. B36, 381 (1987) and Z. Phys. B-Condensed Matter68, 425 (1987)

    Google Scholar 

  34. Yokoyama, H., Shiba, H.: J. Phys. soc. Jpn.56, 1490 (1987) and ibid. J. Phys. soc. Jpn.56, 3582 (1987)

    Google Scholar 

  35. Yokoyama, H., Shiba, H.: J. Phys. Soc. Jpn.56, 3570 (1987)

    Google Scholar 

  36. Gros, C.: (Preprint)

  37. Kasteleijn, P.W.: Physica18, 104 (1952)

    Google Scholar 

  38. Marshall, W.: Proc. R. Soc. A232, 64 (1955)

    Google Scholar 

  39. Thouless, D.J.: Proc. Phys. Soc.90, 243 (1967)

    Google Scholar 

  40. Suzuki, M., Miyashita, S.: Can. J. Phys.56, 902 (1978)

    Google Scholar 

  41. Horsch, P., von der Linden, W.: Physica C: (to be published)

  42. Lee, T.K., von der Linden, W., Horsch, P.: Physica C: (to be published)

  43. Parlett, B.N.: The symmetric eigenvalue problem. Englewood Cliffs, N.J.: Prentice-Hall 1980

    Google Scholar 

  44. Lieb, E., Mattis, D.: J. Math. Phys.3, 749 (1962); Lieb, E., Schultz, T., Mattis, D.: Ann. Phys.16, 407 (1961)

    Google Scholar 

  45. Huse, D.A.: Phys. Rev. B37, 2380 (1988); Huse, D.A., Elser, V.: (Preprint)

    Google Scholar 

  46. Anderson, P.W.: Phys. Rev.86, 694 (1952)

    Google Scholar 

  47. Kubo, R.: Phys. Rev.87, 568 (1952)

    Google Scholar 

  48. Parrinello, M., Arai, T.: Phys. Rev. B10, 265 (1974)

    Google Scholar 

  49. Oguchi, T.: J. Phys. Chem. Solids24, 1649 (1963) and Phys. Rev.117, 117 (1960)

    Google Scholar 

  50. Reger, J.D., Young, A.P.: (Preprint)

  51. Marshall, W., Lovesey, S.W.: Theory of thermal neutron scattering. Oxford: Clarendon Press 1971

    Google Scholar 

  52. Horsch, P., von der Linden, W.: Bull. Am. Phys. Soc.33, 558 (1988)

    Google Scholar 

  53. Cloiseaux des, J., Pearson, J.J.: Phys. Rev.128, 2131 (1962)

    Google Scholar 

  54. Liu, S.: Phys. Rev.142, 267 (1966)

    Google Scholar 

  55. Korringa, J.: Phys. Rev.125, 1972 (1962)

    Google Scholar 

  56. Feynman, R.P.: Phys. Rev.94, 262 (1954)

    Google Scholar 

  57. Girvin, S.M., MacDonald, A.H., Platzman, P.M.: Phys. Rev. Lett.54, 581 (1985) and Phys. Rev. B33, 2481 (1986)

    Google Scholar 

  58. Arovas, D.P., Auerbach, A., Haldane, F.D.M.: Phys. Rev. Lett.60, 531 (1988)

    Google Scholar 

  59. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Phys. Rev. Lett.59, 799 (1987)

    Google Scholar 

  60. Hohenberg, P.C., Brinkmann, W.F.: Phys. Rev. B10, 128 (1974)

    Google Scholar 

  61. Endoh, Y., Shirane, G., Birgeneau, R.J., Richards, P.M., Holt, S.L.: Phys. Rev. Lett.32, 170 (1974)

    Google Scholar 

  62. Lyons, K.B., Fleury, P.A., Schneemeyer, L.F., Waszak, J.V.: Phys. Rev. Lett.60, 732 (1988)

    Google Scholar 

  63. Anderson, P.W.: Phys. Rev. Lett.59, 2497 (1987)

    Google Scholar 

  64. Kitazawa, K.: Physica C: (to be published) and Steglich, F.: Private communication

  65. Chakravarty, S., Halperin, B.I., Nelson, D.R.: (Preprint)

  66. Manousakis, E., Salvador, R.: Phys. Rev. Lett.60, 840 (1988)

    Google Scholar 

  67. Ogawa, T., Kanda, K., Matsubara, T.: Prog. Theor. Phys.53, 614 (1975)

    Google Scholar 

  68. Tosatti, E., Yu, Lu: Physica C: (to be published)

  69. Schrieffer, J.R., Wen, X-G., Zhang, S.-C.: Phys. Rev. Lett.60, 944 (1988)

    Google Scholar 

  70. Lilly, L., Muramatsu, A., Hanke, W.: (Preprint)

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  1. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-7000, Stuttgart, Federal Republic of Germany

    P. Horsch & W. von der Linden

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  1. P. Horsch
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Horsch, P., von der Linden, W. Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice. Z. Physik B - Condensed Matter 72, 181–193 (1988). https://doi.org/10.1007/BF01312134

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  • DOI: https://doi.org/10.1007/BF01312134

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