Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model

TL;DR

This study uses the dynamical vertex approximation to compare antiferromagnetic fluctuations in 2D and 3D Hubbard models, revealing stronger effects and pseudogap formation in two dimensions, with implications for layered materials.

Contribution

It provides a detailed analysis of how antiferromagnetic fluctuations differently affect spectral properties in 2D and 3D Hubbard models using DΓA with a λ correction.

Findings

Stronger impact of spin fluctuations in 2D leading to pseudogap formation.

Suppression of quasiparticle weight more pronounced in 3D.

Pronounced k-dependence of self-energy in 2D observed in spectra.

Abstract

We use the dynamical vertex approximation (D$\Gamma$A) with a Moriyaesque $% \lambda$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The $\mathbf{k}$-dependence of the self energy appears to be also much more pronounced in two dimensions as can be observed in the $\mathbf{k}$-resolved D$\Gamma$A spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.