Ferromagnetism and non-local correlations in the Hubbard model

TL;DR

This paper investigates band-ferromagnetism in the 3D Hubbard model, emphasizing the role of non-local correlations and their impact on spectral properties, phase stability, and optical conductivity.

Contribution

It introduces a non-local self-energy within modified perturbation theory and demonstrates its significance for ferromagnetism, spectral features, and the Mermin-Wagner theorem in the Hubbard model.

Findings

Non-local correlations are crucial for the stability of ferromagnetism.

The phase diagram shows regions of ferromagnetic order in the 3D lattice.

Non-local self-energy affects optical conductivity, canceling the Drude peak.

Abstract

We study the possibility and stability of band-ferromagnetism in the single-band Hubbard model for the simple cubic (SC) lattice. A non-local self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of k-dependence. The importance of non-local correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase digram showing regions of ferromagnetic order is calculated for the three dimensional lattice. Besides, we show results for the optical conductivity and prove that already the renormalized one-loop contribution to the conductivity cancels the Drude peak exactly in case of a local self-energy which is not anymore true for a non-local self-energy.