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Quantum size effects in the attractive hubbard model

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Zeitschrift für Physik B Condensed Matter

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Abstract

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.

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References

  1. Theories of high temperature superconductivity. Halley, J.W. (ed.). Reading: Addison-Wesley 1988

    Google Scholar 

  2. Hubbard, J.: Proc. R. Soc. London Ser. A276, 238 (1963)

    Google Scholar 

  3. Strong correlations and superconductivity. Fukuyama, H., Maekawa, S., Malozemoff, A.P. (eds.). Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

  4. Quantum simulations. Karlsson, J., Doll, J.D., Gubernatis, J.E. (eds.). Singapore: World Scientific Publishing 1990

    Google Scholar 

  5. Moreo, A., Scalapino, D.J.: Phys. Rev. B43, 8211 (1991)

    Google Scholar 

  6. Gor'kov, L.P.: JETP34, 505 (1958)

    Google Scholar 

  7. Nozières, P., Schmitt-Rink, S.: J. Low Temp. Phys.59, 195 (1985)

    Google Scholar 

  8. Jain, K.P., Ramakumar, R., Chancey, C.C.: Physica C168, 297 (1990)

    Google Scholar 

  9. Micnas, R., Ranninger, J., Robaszkiewicz, S.: Rev. Mod. Phys.62, 113 (1990)

    Google Scholar 

  10. Scalettar, R.T., Loh, E.Y., Gubernatis, J.E., Moreo, A., White, S.R., Scalapino, D.J., Sugar, R.L., Dagotto, E.: Phys. Rev. Lett.62, 1407 (1989)

    Google Scholar 

  11. Moreo, A., Scalapino, D.J.: Phys. Rev. Lett.66, 946 (1991)

    Google Scholar 

  12. Shiba, H.: Progr. Theor. Phys.48, 2171 (1972)

    Google Scholar 

  13. Emery, V.J.: Phys. Rev. B14, 2989 (1976)

    Google Scholar 

  14. Yang, C.N.: Phys. Rev. Lett.63, 2144 (1989)

    Google Scholar 

  15. Singh, R.R.P., Scalettar, R.T.: Phys. Rev. Lett.66, 3203 (1991)

    Google Scholar 

  16. Friedel, J.: J. Phys. (Paris)49, 1561 (1988)

    Google Scholar 

  17. Barber, M.N.: In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.), Vol. 8. London: Academic Press 1983

    Google Scholar 

  18. Privman, V.: In: Finite size scaling and numerical simulation of statistical systems. Privman, V. (ed.). Singapore: World Scientific 1990

    Google Scholar 

  19. Loh, E.Y., Gubernatis, J.E.: In: Electrons phase transitions. Hanke, W., Kopaev, Y.V. (eds.). New York: North Holland Physics, Elsevier 1990

    Google Scholar 

  20. Ring, P., Schuck, P.: The nuclear many-body problem. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  21. Perenboom, J.A.A.J., Wyder, P., Meier, F.: Phys. Rep.78, 173 (1981)

    Google Scholar 

  22. Halperin, P.W.: Rev. Mod. Phys.58, 533 (1986)

    Google Scholar 

  23. Goehlich, H., Lange, T., Bergmann, T., Martin, T.P.: Phys. Rev. Lett.65, 748 (1990)

    Google Scholar 

  24. Bormann, D., Schneider, T., Frick, M.: Europhys. Lett.14, 101 (1991)

    Google Scholar 

  25. White, S.R., Scalapino, D.J., Sugar, R.L., Bickers, N.E., Scalettar, R.T.: Phys. Rev. B39, 839 (1989)

    Google Scholar 

  26. Yang, C.N.: Rev. Mod. Phys.34, 694 (1962)

    Google Scholar 

  27. Rogovin, D., Scully, M.: Phys. Rep.25, 175 (1976)

    Google Scholar 

  28. Hamermesh: Group theory and its applications to physical problems. Reading: Addison-Wesley 1962

    Google Scholar 

  29. Gennes, P.G. de: Superconductivity of metals and alloys, p. 108. New York, Amsterdam: W.A. Benjamin Inc. 1966

    Google Scholar 

  30. Anderson, P.W.: J. Phys. Chem. Solids11, 26 (1959)

    Google Scholar 

  31. Mühlschlegel, B.: In: Percolation, localization and superconductivity. Goldman, A.M., Wolf, S.A. (eds.). New York: Plenum Press 1984

    Google Scholar 

  32. Reichl, L.E.: A modern course in statistical physics. Austin: Univ. of Texas Press 1980

    Google Scholar 

  33. Kawabata, A.: Surf. Sci.106, 358 (1981)

    Google Scholar 

  34. Mühlschlegel, B.: Surf. Sci.106, 350 (1981)

    Google Scholar 

  35. Kerman, A.K., Lawson, R.D., Macfarlane, M.H.: Phys. Rev.124, 162 (1961)

    Google Scholar 

  36. Dietrich, K., Mang, H.J., Pradal, J.H.: Phys. Rev.135, P22 (1964)

    Google Scholar 

  37. Iwamoto, F., Onishi, H.: Progr. Theor. Phys.37, 682 (1967)

    Google Scholar 

  38. Linden, W. v.d., Morgenstern, I., Raedt, H. de: Phys. Rev. B41, 4669 (1990)

    Google Scholar 

  39. Frick, M., Linden, W. v.d., Morgenstern, I., Raedt, H. de: Z. Phys. B—Condensed Matter81, 327 (1990)

    Google Scholar 

  40. Koonin, S.E., Sugiyama, G., Friederich, H.: Proceedings of the International Symposium, Bad Honnef 1982, p. 214. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  41. Hirsch, J.E.: Phys. Rev. B28, 4059 (1983)

    Google Scholar 

  42. Chao, K.A., Micnas, R., Robaszkiewicz, S.: Phys. Rev. B30, 4741 (1979)

    Google Scholar 

  43. Bormann, D.: (in preparation)

  44. Huse, D.A.: Phys. Rev. B37, 2380 (1988)

    Google Scholar 

  45. Neuberger, H., Ziman, T.: Phys. Rev. B39, 2608 (1989)

    Google Scholar 

  46. Ceperley, D.M., Alder, B.J.: Phys. Rev. B36, 2092 (1987)

    Google Scholar 

  47. See e.g. [17] Sects. II.A–II.C and [18], Sect. 2.5

    Google Scholar 

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Authors and Affiliations

  1. IBM Research Division, Zürich Research Laboratory, CH-8803, Rüschlikon, Switzerland

    D. Bormann, T. Schneider & M. Frick

  2. Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, W-6900, Heidelberg, Germany

    D. Bormann

  3. Physics Department, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    M. Frick

Authors
  1. D. Bormann
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  2. T. Schneider
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  3. M. Frick
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Bormann, D., Schneider, T. & Frick, M. Quantum size effects in the attractive hubbard model. Z. Physik B - Condensed Matter 87, 1–14 (1992). https://doi.org/10.1007/BF01308251

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  • DOI: https://doi.org/10.1007/BF01308251

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