Abstract
We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional 1/r-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for halffilled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the 1/r-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. It is thus seen that neither Hartree-Fock nor an energetically excellent Jastrow-type wave function yield a reliable prediction on the zero temperature phase transition in the one-dimensional 1/r-Hubbard chain.
Similar content being viewed by others
References
Penn, D.R.: Phys. Rev.142, 350 (1966); Langer, W., Plischke, M., Mattis, D.: Phys. Rev. Lett.23, 1448 (1969); Dichtel, K., Jelitto, R.J., Koppe, H.: Z. Phys.246, 248 (1971)
Gutzwiller, M.C.: Phys. Rev. Lett.10, 159 (1963); Phys. Rev. A134, 923 (1964)
Fulde, P.: Electron correlations in moleculs and solids (Springer Series in Solid State Sciences, Vol. 100), Berlin, Heidelberg, New York: Springer 1991
Feenberg, E.: Theory of quantum fluids. New York: Academic Press 1969; Campbell, C.E.: In: Progress in liquid physics. Croxton, C.A. (ed.), p. 213, New York, Wiley 1978
Gebhard, F., Ruckenstein, A.E.: Phys. Rev. Lett.68, 244 (1992)
Hubbard, J.: Proc. R. Soc. London Ser. A276, 238 (1963); Kanamori, J.: Prog. Theor. Phys.30, 275 (1963)
Haldane, F.D.M.: Phys. Rev. Lett.60, 635 (1988); Shastry, B.S.: Phys. Rev. Lett.60, 639 (1988)
Gebhard, F., Girndt, A., Ruckenstein, A.E.: (in preparation)
Lieb, E.H., Wu, F.Y.: Phys. Rev. Lett.20, 1445 (1968)
Metzner, W., Vollhardt, D.: Phys. Rev. Lett.59, 121 (1987); Phys. Rev. B37, 7382 (1988)
Gebhard, F., Vollhardt, D.: Phys. Rev. Lett.59, 1472 (1987); Phys. Rev. B38, 6911 (1988)
For a short review on Gutzwiller-correlated wave functions, see Vollhardt, D., Dongen, P.G.J. van, Gebhard, F., Metzner, W.: Mod. Phys. Lett. B4, 499 (1990)
Metzner, W., Vollhardt, D.: Phys. Rev. Lett.62, 324 (1989)
Gebhard, F.: Phys. Rev. B41, 9452 (1990)
Strack, R., Vollhardt, D.: Mod. Phys. Lett. B5, 1377 (1991); J. Low. Temp. Phys.84, 357 (1991)
Gebhard, F.: Phys. Rev. B44, 992 (1991)
Baeriswyl, D.: In: Nonlinearity in condenset matter (Springer Series in Solid State Sciences, Vol. 69). Bishop, R., et al. (eds.), p. 183, Berlin, Heidelberg, New York: Springer 1987
See, for example, Uhrig, G.: Phys. Rev. B45, 4738 (1992), and references therein; note that these considerations have to be modified for the case of long-range exchange; the results still hold in one dimension
Brinkman, W.F., Rice, T.M.: Phys. Rev. B2, 4302 (1970)
vollhardt, D.: Rev. Mod. Phys.56, 99 (1984)
Dongen, P.G.J. van, Gebhard, F., Vollhardt, D.: Z. Phys. B76, 199 (1989)
Kaplan, T.A., Horsch, P., Fulde, P.: Phys. Rev. Lett.49, 889 (1982); Yokoyama, H., Shiba, H.: J. Phys. Soc. Jpn.56, 1490 (1987); Gros, C., Joynt, R., Rice, T.M.: Phys. Rev. B36, 381 (1987)
Haldane, F.D.M.: J. Phys. C14, 2585 (1981); Phys. Rev. Lett.45, 1358 (1980);47, 1840 (1981)
In Refs. 5, 8 we used this pictorial representation for eigenstates of the effective Hamiltonian while we use it here for the representation of eigenstates of the kinetic energy operator