Ferromagnetism and Skyrmions in the Hofstadter-Fermi-Hubbard Model

TL;DR

This paper investigates the emergence of ferromagnetism and skyrmions in the Hofstadter-Fermi-Hubbard model using large-scale simulations, revealing quantum Hall ferromagnetism, skyrmion-like excitations, and the effects of magnetic fields on flat-band ferromagnetism.

Contribution

The study demonstrates the presence of lattice quantum Hall ferromagnetism and skyrmion-like excitations in the Hofstadter-Fermi-Hubbard model through DMRG simulations, linking it to experimental ultracold atom systems.

Findings

Identification of quantum Hall ferromagnetism at filling factor ν=1.

Observation of skyrmion-like quasi-particles and quasi-holes.

Prediction of flat-band ferromagnetism breakdown at high magnetic fields.

Abstract

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model using ultracold atoms. We demonstrate, by performing large-scale DMRG simulations, that this model exhibits a lattice analog of the quantum Hall ferromagnet at magnetic filling factor $\nu=1$. We reveal the nature of the low energy spin-singlet states around $\nu\approx1$ and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice quantum Hall ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high-$T_{\rm c}$ superconductivity.