Nagaoka polarons and ferromagnetism in Hubbard models

The search for elusive Nagaoka-type ferromagnetism in the Hubbard model has recently enjoyed renewed attention with the advent of a variety of experimental platforms, including ultracold atoms in optical lattices. Here, we demonstrate a universal mechanism for Nagaoka ferromagnetism (that applies to both bipartite and nonbipartite lattices) based on the formation of ferromagnetic polarons consisting of a dopant dressed with polarized spins. We present a comprehensive study of the ferromagnetic polaron in an electron-doped Hubbard model, establishing various polaronic properties such as its size and energetics. Moreover, we systematically probe the internal structure of the magnetic state—through the use of pinning fields and three-point spin-charge-spin correlation functions—for both the single-polaron limit and the high-density regime of interacting polarons. Our results highlight the crucial role of mobile polarons in the birth of global ferromagnetic order from local ferromagnetism and provide a unified framework to understand the development and demise of the Nagaoka-type ferromagnetic state across dopings.