Non-perturbative approaches to magnetism in strongly correlated electron systems

TL;DR

This paper investigates the microscopic mechanisms stabilizing itinerant ferromagnetism in strongly correlated electron systems using rigorous methods and quantum Monte Carlo simulations, highlighting the roles of exchange interactions, band structure, and degeneracy.

Contribution

It introduces a comprehensive analysis combining rigorous methods and dynamical mean-field theory to understand ferromagnetism in correlated electrons, emphasizing the effects of exchange, degeneracy, and lattice structure.

Findings

Ferromagnetism is stable in the Hubbard model for certain lattices at appropriate densities and large U.

Weak exchange interactions and band degeneracy significantly lower the critical U for ferromagnetism.

Hubbard model with easy axis explains metamagnetism in anisotropic antiferromagnets.

Abstract

The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough $U$. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of $U$ above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.