Gutzwiller Approximation in Degenerate Hubbard Models

TL;DR

This paper applies the Generalized-Gutzwiller-Approximation to degenerate Hubbard models, revealing how the metal-insulator transition depends on electron filling, degeneracy, and lattice structure, and deriving a general expression for the critical interaction.

Contribution

It introduces a comprehensive derivation of the critical interaction $U_c$ for metal-insulator transitions in degenerate Hubbard models, unifying previous Gutzwiller solutions.

Findings

Metal-insulator transition occurs at finite $U_c$ for integer fillings.

$U_c$ depends on band degeneracy $N$ and filling $x$.

Derived a general expression for $U_c(x,N)$ that includes previous models.

Abstract

Degenerate Hubbard models are studied using the Generalized-Gutzwiller-Approximation. It is found that the metal-insulator transition occurs at a finite correlation $U_c$ when the average number of electrons per lattice site is an integer. The critical $U_c$ depends sensitively on both the band degeneracy $N$ and the filling $x$. A derivation is presented for the general expression of $U_c(x,N)$ which reproduces all previously known Gutzwiller solutions, including that of the Boson Hubbard model. Effects of the lattice structure on the metal-insulator transition and the effective mass are discussed.