The Moment Sum Rule and Its Consequences for Ferromagnetism in the Hubbard Model

Abstract

The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m 3 is conceptually important for a qualitatively correct description of the quasi-particle band structure in the strong-correlation regime. Different analytical approximations for the self-energy are analyzed with respect to their compatibility with the moment sum rule. To estimate the practical usefulness of the sum rule, correlation functions and dynamical quantities are determined. The results obtained within the various approximation schemes of different complexity are compared with each other and also with essentially exact results available for infinite-dimensional lattices. It turns out that the m 3 moment is rather unimportant for the paramagnetic phase on the hyper-cubic lattice. Contrary, it decisively influences the magnetic phase boundary as well as the critical temperature for the ferromagnetic phase on an f.c.c.-type lattice.

Ferromagnetism in the periodic Anderson model. A comparison of spectral density approximation (SDA), modified alloy analogy (MAA) and modified perturbation theory (MPT)

“…One observes a reduction of the ferromagnetic region compared to the SDA result. So, similar to the Hubbard model [30,49], quasiparticle damping is unfavourable for ferromagnetism. However, apart from the lower critical n (tot) , the MAA and SDA curves are very similar.…”

Stabilization ofd-band ferromagnetism by hybridization with uncorrelated bands

“…This is, however, the interesting case concerning band-ferromagnetism. For the single-band model in the limit of infinite spatial dimensions the theories are thoroughly tested against numerical exact results available in this limit 23 . It is found that the SDA as well as the MAA systematically overestimate magnetic quantities such as the Curie temperature but turn out to give a qualitative satisfying description of band-ferromagnetism 23 17 .…”

Pseudospin-electron model spectrum in alloy analogy approximation

“…Terms of the R 14 (1)↑ (ω) and R 14 (2)↑ (ω) type are taken into consideration in different ways in various approximations. For example, in Hubbard-III approximation only the first of them is included [5,9]. In this work we use the alloy analogy approximation; in this case terms (64, 65) are neglected (see [9]).…”