How correlations change the magnetic structure factor of the kagome Hubbard model

TL;DR

This study explores how electronic correlations influence the magnetic structure factor in the kagome Hubbard model across different regimes, revealing a crossover in magnetic correlations near the metal-insulator transition without magnetic ordering.

Contribution

It provides a comprehensive analysis of magnetic correlations in the kagome Hubbard model using three advanced numerical methods, filling gaps in understanding the weakly and moderately correlated regimes.

Findings

No magnetic ordering tendencies in the kagome Hubbard model.

Magnetic correlations show a crossover near the metal-insulator transition.

Magnetic correlations remain short-range even close to the transition.

Abstract

The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMFT), the dynamical vertex approximation (D$\Gamma$A), and determinant quantum Monte Carlo (DQMC). In contrast to the archetypal square-lattice, we find no tendencies towards magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does however not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials.