https://doi.org/10.1007/s100510050030
"Linearized"dynamical mean-field theory for the Mott-Hubbard transition
1
Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universität
Augsburg,
86135 Augsburg, Germany
2
Theoretische Festkörperphysik, Institut für Physik, Humboldt-Universität zu
Berlin,
10115 Berlin, Germany
Received:
6
May
1999
Revised:
2
July
1999
Published online: 15 January 2000
The Mott-Hubbard metal-insulator transition is studied within a simplified version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between the impurity level and the conduction band is approximated by a single pole at the Fermi energy. In this approach, the DMFT equations are linearized, and the value for the critical Coulomb repulsion Uc can be calculated analytically. For the symmetric single-band Hubbard model at zero temperature, the critical value is found to be given by 6 times the square root of the second moment of the free (U=0) density of states. This result is in good agreement with the numerical value obtained from the Projective Selfconsistent Method and recent Numerical Renormalization Group calculations for the Bethe and the hypercubic lattice in infinite dimensions. The generalization to more complicated lattices is discussed. The "linearized DMFT"yields plausible results for the complete geometry dependence of the critical interaction.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.27.+a – Strongly correlated electron systems; heavy fermions / 71.30.+h – Metal-insulator transitions and other electronic transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
