The Metal-Insulator Transition in the Doubly Degenerate Hubbard Model

TL;DR

This paper investigates the metal-insulator transition in the doubly degenerate Hubbard model using slave-boson mean-field theory, providing analytic solutions for infinite interactions and numerical analysis for finite interactions, with implications for real materials.

Contribution

It offers a comprehensive analysis of the MI transition in the DHM, including exact solutions in the infinite interaction limit and numerical results for finite interactions, linking theory to experimental observations.

Findings

Mass-enhancement factor diverges at integer fillings.

The N dependence of Z matches the observed specific-heat coefficient in Sr_{1-x}La_xTiO_3.

Analytic solutions are obtained for the infinite interaction case.

Abstract

A systematic study has been made on the metal-insulator (MI) transition of the doubly degenerate Hubbard model (DHM) in the paramagnetic ground state, by using the slave-boson mean-field theory which is equivalent to the Gutzwiller approximation (GA). For the case of infinite electron-electron interactions, we obtain the analytic solution, which becomes exact in the limit of infinite spatial dimension. On the contrary, the finite-interaction case is investigated by numerical methods with the use of the simple-cubic model with the nearest-neighbor hopping. The mass-enhancement factor, $Z$, is shown to increase divergently as one approaches the integer fillings ($N = 1, 2, 3$), at which the MI transition takes place, $N$ being the total number of electrons. The calculated $N$ dependence of $Z$ is compared with the observed specific-heat coefficient, $\gamma$, of $Sr_{1-x}La_xTiO_3$ which is reported to significantly increase as $x$ approaches unity.