Polaronic mechanism of Nagaoka ferromagnetism in Hubbard models

The search for elusive Nagaoka ferromagnetism in the Hubbard model has recently enjoyed renewed attention with the advent of a variety of platforms enabling its realization. These include moiré materials, quantum dots, and ultracold atoms in optical lattices. Using large-scale density-matrix renormalization group (DMRG) calculations, we present a comprehensive investigation of the Nagaoka polaron problem in a Hubbard model, without simplification to the t-J limit. Our results show a universal mechanism for Nagaoka ferromagnetism that proceeds via the formation of ferromagnetic polarons, consisting of a dopant dressed with polarized spins that applies to both bipartite and non-bipartite lattices. We establish this by systematically using a judicious application of pinning fields, and studying three-point spin-charge-spin correlation functions in both the single-polaron limit as well as the higher-density regime of interacting polarons. Finally, we extend our calculations to study ferromagnetism in an extended Hubbard model, with long-range electron-electron interactions, needed to study arrays of gate-defined semiconductor quantum dots.