Abstract
The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.
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Clark, J.W., Ristig, M.L.: In: Momentum distributions. Silver, R.N. (ed.). New York: Plenum 1989
Dabringhaus, A., Ristig, M.L.: In: Condensed matter theories. Keller, J. (ed), Vol. 4. New York: Plenum 1989
Fantoni, S., Wang, X., Tosatti, E., Lu Yu: Physica C153–155, 1255 (1988)
Hubbard, J.: Proc. R. Soc. London Ser. A276, 238 (1963)
Anderson, P.W.: Science235, 1196 (1987)
Anderson, P.W.: In: Proceedings of the International School of Physics “Enrico Fermi” Course CIV, Varenna 1987. Broglia, R.A., Schrieffer, J.R. (eds.). Amsterdam: North Holland 1988
Metzner, W., Vollhardt, D.: Phys. Rev. Lett.59, 121 (1987)
Metzner, W., Vollhardt, D.: Phys. Rev. B37, 7382 (1988)
Gros, C., Rice, T.M., Joynt, R.: In: Recent progress in many-body theories. Kallio, A.J., Pajanne, E., Bishop, R.F. (eds.), Vol. 1, New York: Plenum 1988
Fazekas, P.: In: Recent progress in many-body theories. Kallio, A.J., Pajanne, E., Bishop, R.F. (eds.), Vol. 1. New York: Plenum 1988
Hirsch, J.E.: Phys. Rev. Lett.54, 1317 (1985)
Hirsch, J.E.: Phys. Rev. B31, 4403 (1985)
Coppersmith, S.N., Yu, C.C.: Phys. Rev. B39, 11464 (1989)
Ristig, M.L., Lam, P.M.: J. Low Temp. Phys.40, 571 (1980)
Ristig, M.L., Kürten, K.E., Clark, J.W.: Phys. Rev. B19, 3539 (1979)
Kürten, K.E., Campbell, C.E.: J. Low Temp. Phys.44, 149 (1981)
Lam, P.M., Ristig, M.L.: Kinam1, 407 (1979)
Lantto, L.J.: Phys. Rev. B22, 1380 (1980)
Gutzwiller, M.C.: Phys. Rev. Lett.10, 159 (1963)
Penn, D.R.: Phys. Rev.142, 350 (1966)
Clark, J.W.: Nucl. Phys. A328, 587 (1979)
Viviani, M., Buendia, E., Fantoni, S., Rosati, S.: Phys. Rev. B38, 4523 (1988)
Fantoni, S., Viviani, M.: In: Spin polarized quantum systems. Stringari, J.S.J.-S. (eds.), Singapore: World Scientific 1989
Gutzwiller, M.C.: Phys. Rev.134, A923 (1964)
Gutzwiller, M.C.: Phys. Rev.137, A1726 (1965)
Feenberg, E.: Theory of quantum fluids. New York: Academic 1969
Clark, J.W.: In: Progress in particle and nuclear physics. Wilkinson, D.H. (ed.), Vol. 2. Oxford: Pergamon 1979
Ristig, M.L., Clark, J.W.: Phys. Rev. B 1990 (in press)
Rosati, S.: In: From nuclei to particles. Proceedings of the International School of Physics “Enrico Fermi” Course LVII, Varenna 1981. Molinari, A. (ed.). Amsterdam: North-Holland 1982
Ristig, M.L.: In: From nuclei to particles. Proceedings of the International School of Physics “Enrico Fermi” Course LVII, Varenna 1981. Molinari, A. (ed.), Amsterdam: North-Holland 1982
Ristig, M.L., Clark, J.W.: Phys. Rev. B14, 2875 (1976)
Fantoni, S.: Nuovo Cimento A44, 191 (1978)
Clark, J.W., Ristig, M.L.: In: The nuclear many-body problem. Calogero, F., Ciofi degli Atti, C. (eds.). Bologna: Editrice Compositori 1973
Mayer, J.E., Mayer, M.G.: Statistical mechanics. New York: Wiley 1940
Horsch, P.: Phys. Rev. B24, 7351 (1981)
Razafimandimby, H.A.: Z. Phys. B — Condensed Matter49, 33 (1982)
Zabolitzky, J.G.: Phys. Rev. A16, 1258 (1977)
Kürten, K.E., Clark, J.W.: Phys. Rev. B30, 1342 (1984)
Panoff, R.M.: In: Condensed matter theories. Vashishta, P., Kalia, R.K., Bishop, R.F. (eds.), Vol. 2. New York: Plenum 1987
Usmani, Q.N., Friedman, B., Pandharipande, V.R.: Phys. Rev.B25, 4502 (1982)
Viviani, M., Buendia, E., Fabrocini, A., Rosati, S.: Nuovo Cimento8D, 561 (1986)
Van Leeuwen, J.M.J., Groeneveld, J., De Boer, J.: Physica25, 792 (1959)
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Ristig, M.L. Correlated ground state of the Hubbard model. Z. Physik B - Condensed Matter 79, 351–359 (1990). https://doi.org/10.1007/BF01437644
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DOI: https://doi.org/10.1007/BF01437644