Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches

TL;DR

This paper compares Hartree-Fock and slave-boson methods to analyze magnetic phases in the Hubbard model, revealing how correlations suppress certain magnetic states and highlighting the importance of phase separation near half-filling.

Contribution

It provides a comprehensive comparison of mean-field and slave-boson approaches in predicting magnetic phases, including spiral and phase separation effects, in the Hubbard model.

Findings

Correlation effects suppress ferromagnetism and spiral states without nesting.

Magnetic phase separation is significant near half-filling.

Wide phase regions of magnetic states occur close to half-filling.

Abstract

The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard $U$ by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.