Ferromagnetism and skyrmions in the Hofstadter-Fermi-Hubbard model

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 density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor nu = 1. We reveal the nature of the low energy spin-singlet states around nu asymptotic to 1 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 QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- T-c superconductivity.

Automated summary

Strongly interacting fermionic systems can exhibit interesting quantum many-body states with exotic excitations. This study focuses on the interplay between strong interactions and the Pauli exclusion principle in the Hofstadter-Fermi-Hubbard model. The researchers discover a lattice analog of the quantum Hall ferromagnet at magnetic filling factor nu = 1, and observe spin-singlet states with spin-spin correlations similar to skyrmions. They also predict the breakdown of flat-band ferromagnetism at large fields. This work opens up possibilities for experimental studies of lattice QH ferromagnetism and its relation to high-Tc superconductivity.