``Linearized'' Dynamical Mean-Field Theory for the Mott-Hubbard transition

TL;DR

This paper introduces a simplified, linearized version of Dynamical Mean-Field Theory to analytically determine the critical Coulomb repulsion for the Mott-Hubbard transition, aligning well with numerical methods.

Contribution

It presents a linearized DMFT approach that allows analytical calculation of the critical U for the Mott transition, improving understanding of lattice geometry effects.

Findings

Analytical expression for critical U in symmetric Hubbard model.

Good agreement with numerical methods like NRG and Projective Selfconsistent Method.

Extension discussion to complex lattice geometries.

Abstract

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 U_{\rm c} 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.