Antiferromagnetism of almost localized fermions: Evolution from Slater-type to Mott-Hubbard gap

TL;DR

This paper analyzes the evolution of the magnetic gap in the Hubbard model, highlighting the transition from Slater to Mott-Hubbard gaps and examining correlation effects on effective mass and gap contributions.

Contribution

It provides a detailed discussion of the magnetic gap evolution and correlation effects using the slave boson approach, contrasting with paramagnetic cases and infinite-dimensional solutions.

Findings

Magnetic (Slater) gap evolves into Mott-Hubbard gap with correlations.

Weak renormalization of effective mass in half-filled band case.

Strong effective mass enhancement in non-half-filled band case.

Abstract

We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made.