Quantum Hall Ferromagnetism and Skyrmions in the Hubbard-Hofstadter Model

It has been suggested that quantum Hall ferromagnetism at odd integer Landau filling factors and associated skyrmion excitations arise in the fermionic Hubbard-Hofstadter model. But current evidence for the existence of skyrmions and their region of stability in phase space is not conclusive. In this work, we use determinant quantum Monta Carlo to study the spin and charge correlations of the Hubbard-Hofstadter model on a triangular lattice to demonstrate the existence of both quantum Hall ferromagnetism and nearby skyrmionic states. We consider the effect of changing the relative strengths of Coulomb repulsion, orbital coupling and Zeeman coupling. Our study is relevant for understanding the behavior of strongly correlated electrons under large magnetic fields, particularly in bilayer TMD Moiré materials.