Itinerant ferromagnetism in the Hubbard model

The Hubbard model, a key descriptor of strongly interacting electronic systems, typically features antiferromagnetic spin alignment. However, in certain idealized limits, the celebrated Nagaoka theorem predicts a ferromagnetic ground state, realizing which has been a long-standing challenge in condensed matter physics. In this talk, we describe how itinerant ferromagnetism arises in a variety of systems without the (infeasible) constraints required by the Nagaoka theorem. Using large-scale density-matrix renormalization group calculations, we first identify high-spin ground states of the Hubbard model on finite-sized triangular and square lattices and uncover their microscopic kinetic origins. Furthermore, we develop a universal mechanism for such Nagaoka ferromagnetism based on the formation of ferromagnetic polarons consisting of a dopant dressed with polarized spins. Probing the polaronic structure and dynamics using multibody correlation functions and pinning fields, we establish the crucial role of mobile polarons in the birth of global long-range order from local ferromagnetic correlations. Finally, we consider a generalization of the Hubbard model which includes the effects of Coulomb interactions and show how long-range interactions induce an instability of high-spin states towards phase separation and competing stripe orders. Our results find immediate application to several experimental systems including moiré materials, ultracold atoms, and quantum dot arrays, providing new insights into recent observations as well as proposals for future experiments.