Ferromagnetism in the t-t' Hubbard model: interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme

TL;DR

This paper investigates ferromagnetism in the Hubbard model across different lattices using a Goldstone-mode preserving scheme, revealing how lattice structure, band dispersion, and interactions influence magnetic stability.

Contribution

It introduces a systematic inverse-degeneracy expansion that explicitly preserves spin-rotation symmetry and the Goldstone mode, providing new insights into ferromagnetism stability in the Hubbard model.

Findings

Ferromagnetism is favored in the Hubbard model with asymmetric, peaked DOS near band edges.

Magnon energies and $T_c$ behavior agree with DMFT results for certain densities.

Long-wavelength fluctuations significantly reduce the stable density range for ferromagnetism.

Abstract

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy ($1/{\cal N}$) expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the DOS is sufficiently asymmetric and strongly peaked near band edge, as for fcc lattice with finite $t'$. For short-wavelength modes, behavior of a characteristic energy scale $\omega^* \sim T_c$ (magnon-DOS-peak energy) is in excellent agreement with the $T_c$ vs. $n$ behavior within DMFT, both with respect to the stable range of densities ($0.20 < n < 0.85$) as well as the optimal density $n=0.65$. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.