Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers

TL;DR

This study uses quantum Monte Carlo simulations to reveal that interacting electrons on a honeycomb lattice can spontaneously form ferromagnetic insulating states with odd Chern numbers, aligning with experimental observations in moiré systems.

Contribution

It demonstrates the emergence of spontaneous ferromagnetic insulating states with odd Chern numbers in a Hubbard model on a honeycomb lattice, a novel finding in quantum Hall systems.

Findings

Emergence of antiferromagnetic insulator at half-filling

Observation of odd Chern number states with ferromagnetic correlations

Qualitative agreement of Hofstadter spectrum with experiments

Abstract

Motivated by recent experimental work on moir\'e systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence $\pm (2N+1)$. These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction.