Slave-Boson Functional-Integral Approach to the Hubbard Model with Orbital Degeneracy

TL;DR

This paper develops a slave-boson functional-integral method for the Hubbard model with orbital degeneracy, providing analytical and numerical insights into the metal-insulator transition influenced by exchange interactions.

Contribution

It introduces a new slave-boson functional-integral approach applicable to models with arbitrary orbital degeneracy, extending the Gutzwiller approximation to multi-orbital systems.

Findings

Analytical expressions for the critical interaction for MI transition.

Numerical results for the doubly degenerate model in paramagnetic states.

Discussion of exchange interaction effects on the MI transition.

Abstract

A slave-boson functional-integral method has been developed for the Hubbard model with arbitrary, orbital degeneracy $D$. Its saddle-point mean-field theory is equivalent to the Gutzwiller approximation, as in the case of single-band Hubbard model. Our theory is applied to the doubly degenerate ($D = 2$) model, and numerical calculations have been performed for this model in the paramagnetic states. The effect of the exchange interaction on the metal-insulator (MI) transition is discussed. The critical interaction for the MI transition is analytically calculated as functions of orbital degeneracy and electron occupancy.