The moment sum rule and its consequences for ferromagnetism in the Hubbard model

TL;DR

This paper investigates the importance of the spectral density sum rule up to the third moment in the Hubbard model, showing its critical role in accurately describing ferromagnetism and phase boundaries in strongly correlated systems.

Contribution

It demonstrates that respecting the m=3 moment sum rule is essential for correct ferromagnetic phase predictions in the Hubbard model, especially on fcc lattices.

Findings

The m=3 moment is crucial for ferromagnetic phase boundary accuracy.

Different approximation schemes are compared against exact results.

Respecting the sum rule improves the qualitative description of the quasi-particle band.

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 fcc-type lattice.