Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model

While the exact phase diagram of the Fermi-Hubbard model remains poorly understood despite decades of progress, nearly 60 years ago, Nagaoka proved that a single dopant in an otherwise half-filled Hubbard system can bring about ferromagnetism through kinetic means. The phenomenon was recently observed with ultracold atoms in triangular optical lattices. Here, we explore the kinetic ferromagnetism within the square lattice Hubbard model and its strong-coupling counterpart, the $t-J$ model, at finite temperatures in the thermodynamic limit via numerical linked-cluster expansions. We find evidence of ferromagnetic Nagaoka polarons at dopings up to $\sim 30\%$ away from half filling for a variety of interaction strengths and at temperatures as low as $0.2$ of the hopping energy. We map out the boundaries of this phase through analyzing various correlation functions.