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Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach

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Zeitschrift für Physik B Condensed Matter

Abstract

We investigate the ground-state properties of the two-dimensional Hubbard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the strongly correlated electronic system are treated by means of a variational squeezed-polaron wave function proposed by Zheng, where the possibility of static (frozen) phonon-staggered ordering is taken into account. Adapting the Kotliar-Ruckenstein slave boson approach to the effective electronic Hamiltonian, which is obtained in the vacuum state of the transformed phonon subsystem, our theory is evaluated within a two-sublattice saddle-point approximation at arbitrary band-filling over a wide range of electron-electron and electron-phonon interaction strengths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxilary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In order to characterize the crossover from the adiabatic (ω=0) to the nonadiabatic (ω=∞) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (spin) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing ω. As the central result we present the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.

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References

  1. Bednorz, I.G., Müller, K.A.: Z. Phys. B64, 189 (1986)

    Google Scholar 

  2. Rice, T.M., Less, J.: Common Met.164–165, 1439 (1990); Batlogg, B.: Physica B169, 7 (1991); Emery, V.J.: Physica B169, 17 (1991); Fukuyama, H.: Physica C185–189, xxv (1991); Ginzburg, V.L.: Physica C209, 1 (1993)

    Google Scholar 

  3. Tsuda, N., Nasu, K., Yanese, A., Siratori, K.: Electronic Conduction in Oxides. Berlin, Heidelberg, New York Springer 1990

    Google Scholar 

  4. Manh, D., Mayou, D., Cyrot-Lackmann, F.: Europhys. Lett.13, 167 (1990)

    Google Scholar 

  5. Friedl, B., Thomsen, C., Cordona, M.: Phys. Rev. Lett.65, 1990 (1990)

    Google Scholar 

  6. Güttler, B., Salje, E., Freeman, P., Blunt, J., Harris, M., Duffield, T., Ager, C.D., Hughes, H.P.: J. Phys.2, 8977 (1990); Litvinchuk, A.P., Thomson, C., Cordona, M., Stastny, P., Mateev, D.M.: Phys. Rev. B44, 9723 (1991)

    Google Scholar 

  7. Sharma, R.P., Rehn, L.E., Baldo, P.M., Lin, J.Z.: Phys. Rev. Lett.62, 2869 (1989); Haga, T., Yamaya, K., Abe, Y., Tajima, Y., Hidaka, Y.: Phys. Rev B41, 826 (1990)

    Google Scholar 

  8. Egami, T., Toby, B.H., Billinge, S.J.L., Janot, Chr., Jorgenson, J.D., Hinks, D.G., Subramanian, M.A., Crawford, M.K., Farneth, W.E., McCarron, E.M.: In: Electronic Structure and Mechanisms of High Temperature Superconductivity. Ashkenazi, J., Barnes, S.E., Zuo, F., Vezzoli, G., Klein, B.M. (eds.) New York: Plenum Press 1991

    Google Scholar 

  9. Kim, Y.H., Foster, C.M., Heeger, A.J., Cox, S., Stucky, G.: Phys. Rev. B38, 6478 (1988)

    Google Scholar 

  10. Jorgenson, J.D.: Phys. Today44, 34 (1991)

    Google Scholar 

  11. Zhong, J., Schüttler, H.-B.: Phys. Rev. Lett.69, 1600 (1992)

    Google Scholar 

  12. Suzuki, Y.Y., Pincus, P., Heeger, A.J.: Phys. Rev B44, 7127 (1991); Bi, X.-X., Eklund, P.C.: Phys. Rev. Lett.70, 2625 (1993)

    Google Scholar 

  13. Mustre de Leon, J., Batistić, I., Bishop, A.R., Conradson, S.D., Trugman, S.A.: Phys. Rev. Lett.68, 3236 (1992)

    Google Scholar 

  14. Alexandrov, A.S., Ranninger, J.: Phys. Rev. B45, 13109 (1992); Physica C198, 360 (1992)

    Google Scholar 

  15. Hirsch, J.E.: Phys. Rev. B47, 5351 (1993)

    Google Scholar 

  16. Emin, D.: In: Physics of High-Temperature Superconductors, Maekawa, S., Sato, M. (eds.) Berlin, Heidelberg, New York: Springer 1992; Phys. Rev. B45, 5525 (1992)

    Google Scholar 

  17. Verbist, G., Peeters, F.M., Devreese, J.T.: Phys. Scr. T39, 66 (1991)

    Google Scholar 

  18. Cohen, R.E., Pickett, W.E., Krakauer, H.: Phys. Rev. Lett.64, 2575 (1990); Krakauer, H., Pickett, W.E., Cohen, R.E.: Phys Rev. B47, 1002 (1993)

    Google Scholar 

  19. Anisimov, V.I., Korotin, M.A., Zaanen, J., Andersen, O.K.: Phys. Rev. Lett.68, 345 (1992)

    Google Scholar 

  20. Ramšak, A., Horsch, P., Fulde, P.: Phys. Rev. B46, 14305 (1992)

    Google Scholar 

  21. Hirsch, J.E.: Phys. Rev. B.31, 6022 (1985)

    Google Scholar 

  22. Jurczek, E., Rice, T.M.: Europhys. Lett.1, 225 (1986); Prětre, A., Rice, T.M.: J. Phys. C19, 1365 (1986); Prelovšek, P., Rice, T.M., Zhang, F.C.: J. Phys. C20, L229 (1987)

    Google Scholar 

  23. Muramatsu, A., Hanke, W.: Physica C153, 229 (1988)

    Google Scholar 

  24. Zheng, H.: Phys. Rev. B41, 4723 (1990)

    Google Scholar 

  25. Zheng, H., Feinberg, D., Avignon, M.: Phys. Rev. B41, 11557 (1990)

    Google Scholar 

  26. Fehske, H., Ihle, D., Loos, J., Trapper, U., Büttner, H.: Z. Phys. B (submitted for publication)

  27. Das, A.N., Konior, J., Ray, D.K., Oleś, A.M.: Phys. Rev. B44, 7680 (1991)

    Google Scholar 

  28. Batistić, I., Gammel, J.T., Bishop, A.R.: Phys. Rev. B44, 13228 (1992)

    Google Scholar 

  29. Holstein, T.: Ann. Phys.8, 325 (1959); ibid8, 343 (1959)

    Google Scholar 

  30. Hirsch, J.E., Fradkin, E.: Phys. Rev. B27, 4302 (1983)

    Google Scholar 

  31. Marsiglio, F.: Phys. Rev. B42, 2416 (1990)

    Google Scholar 

  32. Scalettar, R.T., Bickers, N.E., Scalapiono, D.J.: Phys. Rev. B40, 197 (1989); Noack, R.M., Scalapino, D.J., Scalettar, R.T.: Phys. Rev. Lett.66, 778 (1991); Velié, M., Noack, R.M., White, S.R.: Phys. Rev. B46, 271 (1992); Noack, R.M., Scalapino, D.J.: Phys. Rev. B47, 305 (1993)

    Google Scholar 

  33. Levine, G., Su, W.P.: Phys. Rev. B42, 4143 (1990)

    Google Scholar 

  34. Aubry, S., Quemerais, P., Raimbault, J.: Proceedings of the Third European Conference on Low Dimensional Superconductors, (Dubrovnik, Yougoslavia 1989)

  35. Suzuki, S., Toyozawa, Y.: J. Phys. Soc. Jpn.59, 2841 (1990)

    Google Scholar 

  36. Raedt, H.D., Lagendijk, A.: Phys. Rev. Lett.49, 1522 (1982)

    Google Scholar 

  37. Toyozawa, Y.: Prog. Theor. Phys.26, 29 (1961)

    Google Scholar 

  38. Emin, D.: Adv. Phys.12, 57 (1973)

    Google Scholar 

  39. Feinberg, D., Ciuchi, S., de Pasquale, F.: Int. J. Mod. Phys. B4, 1317 (1990)

    Google Scholar 

  40. Ranninger, J., Thibblin, U.: Phys. Rev. B45, 7730 (1992)

    Google Scholar 

  41. Fehske, H., Röder, H., Mistriotis, A., Büttner, H.: J. Phys.5, 3565 (1993); Röder, H., Fehske, H., Büttner, H.: Phys. Rev. B47, 12420 (1993)

    Google Scholar 

  42. Das, A.N., Konior, J., Ray, D.K.: Physica C170, 215 (1990)

    Google Scholar 

  43. Schmeltzer, D., Bishop, A.R.: Europhys. Lett.12, 369 (1990)

    Google Scholar 

  44. Fehske, H., Deeg, M., Büttner, H.: Phys. Rev. B46, 3713 (1992)

    Google Scholar 

  45. Deeg, M., Fehske, H., Büttner, H.: Z. Phys. B88, 283 (1992); ibid.91, 31 (1993)

    Google Scholar 

  46. Zheng, H., Feinberg, D., Avignon, M.: Phys. Rev. B39, 9405 (1989)

    Google Scholar 

  47. Kotliar, G., Ruckenstein, A.E.: Phys. Rev. Lett.57, 1362 (1986)

    Google Scholar 

  48. Alexandrov, A.S.: Phys. Rev. B38, 925 (1988)

    Google Scholar 

  49. Lang, I.G., Firsov, Y.A.: Zh. Eksp. Teor. Fiz.43, 1843 (1962)

    Google Scholar 

  50. Zheng, H.: Solid State Commun.65, 731 (1988); Phys. Rev. B37, 7419 (1988); ibid.38, 11865 (1988)

    Google Scholar 

  51. Yuen, H.P.: Phys. Rev. A13, 2226 (1976)

    Google Scholar 

  52. Lo, C.F., Sollie, R.: Phys. Lett. A169, 91 (1992); Phys. Rev. B48, 10183 (1993)

    Google Scholar 

  53. Nasu, K.: Phys. Rev. B35, 1748 (1987)

    Google Scholar 

  54. Barnes, S.E.: J. Phys. F6, 1375 (1976)

    Google Scholar 

  55. Frésard, R., Wölfle, P.: Int. J. Mod. Phys. B5&6, 685 (1992)

    Google Scholar 

  56. Negele, J.W., Orland, H.: Quantum Many-Particle Systems. Reading, Mass Addison Wesley 1988

    Google Scholar 

  57. Li, T., Wölfle P., Hirschfeld, P.J.: Phys. Rev. B40, 6817 (1989)

    Google Scholar 

  58. Frésard, R., Dzierzawa, M., Wölfle, P.: Europhys. Lett.15, 325 (1991); Doll. K., Dzierzawa, M., Frésard, R., Wölfle, P.: Z. Phys. B90, 297 (1993); Arrigoni, E., Strinati, G.C.: Phys. Rev. B44, 7455 (1991)

    Google Scholar 

  59. Rasul, J.W., Li, T.: J. Phys. C21, 5119 (1988); Lavagna, M.: Phys. Rev. B41, 142 (1990); Jolicoeur, T., Guillou, J.C.L.: Phys. Rev. B44, 2403 (1991)

    Google Scholar 

  60. Lilly, L., Muramatsu, A., Hanke, W.: Phys. Rev. Lett.65, 1379 (1990); The authors have performed a comparative study of the two-sublattice SB mean-field theory and quantum MC calculations, where an excellent agreement was obtained for ground-state energy, local magnetic moment and effective hopping matrix element

    Google Scholar 

  61. Oleś, A.M.: J. Phys. C15, L1065 (1982)

    Google Scholar 

  62. Stollhoff, G., Fulde, P.: Z. Phys. B26, 257 (1977)

    Google Scholar 

  63. Weber, S.: Thesis, Universität Bayreuth 1985; Weber, S., Büttner, H.: J. Phys. C17, L337 (1984)

  64. Trapper, U. (unpublished)

  65. Sofo, J.O., Balseiro, C.A.: Phys. Rev. B45, 377 (1992)

    Google Scholar 

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

    Google Scholar 

  67. Emery, V.J., Kivelson, S.A.: Physica C209, 597 (1993)

    Google Scholar 

  68. Ranninger, J., Thibblin, U.: Phys. Rev. B45, 7730 (1992)

    Google Scholar 

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Authors and Affiliations

  1. Physikalisches Institut, Universität Bayreuth, Universitätsstrasse 30, D-95440, Bayreuth, Germany

    U. Trapper, H. Fehske, M. Deeg & H. Büttner

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  1. U. Trapper
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Trapper, U., Fehske, H., Deeg, M. et al. Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: A variational slave boson approach. Z. Physik B - Condensed Matter 93, 465–478 (1994). https://doi.org/10.1007/BF01314251

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  • DOI: https://doi.org/10.1007/BF01314251

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