Slave-Boson Mean-Field Theory of the Antiferromagnetic State in the Doubly Degenerate Hubbard Model - the Half-Filled Case -

TL;DR

This paper uses slave-boson mean-field theory to analyze the antiferromagnetic state in the half-filled doubly degenerate Hubbard model, revealing how electron correlations and exchange interactions influence metal-insulator transitions and magnetic properties.

Contribution

It applies slave-boson mean-field theory to the half-filled doubly degenerate Hubbard model, providing new insights into the effects of electron correlation and exchange interaction on antiferromagnetism.

Findings

No metal-insulator transition except at zero interaction.

Electron correlation reduces the energy gap in the antiferromagnetic insulator.

Exchange interaction J significantly affects magnetic moments and stability.

Abstract

The antiferromagnetic ground state of the half-filled Hubbard model with the doubly degenerate orbital has been studied by using the slave-boson mean-field theory which was previously proposed by the present author. Numerical calculations for the simple cubic model have shown that the metal-insulator transition does not take place except at the vanishing interaction point, in strong contrast with its paramagnetic solution. The energy gap in the density of states of the antiferromagnetic insulator is much reduced by the effect of electron correlation. The exchange interaction $J$ plays an important role in the antiferromagnetism: although for $J = 0$ the sublattice magnetic moment $m$ in our theory is fairly smaller than $m_{HFA}$ obtained in the Hartree-Fock approximation, $m$ for $J/U > 0.2$ ($U$: the Coulomb interaction) is increased to become comparable to $m_{HFA}$. Surprisingly, the antiferromagnetic state is easily destroyed if a small, negative exchange interaction ($J/U < -0.05$) is introduced.