The search for ferromagnetism in the Hubbard model has been a problem of outstanding interest since Nagaoka's original proposal in 1966. Recent advances in quantum simulation have today enabled the study of tunable doped Hubbard models in ultracold atomic systems. Employing large-scale density-matrix renormalization group calculations, we establish the existence of high-spin ground states of the Hubbard model on finite-sized triangular lattices, analyze the microscopic mechanisms behind their origin, and investigate the interplay between ferromagnetism and other competing orders, such as stripes. These results explain (and shed light on) the intriguing observations of ferromagnetic correlations in recent optical-lattice experiments. Additionally, we examine a generalized variant of the Hubbard model, wherein any second electron on a single lattice site is weakly bound compared to the first one, and demonstrate how this modification can lead to enhanced ferromagnetism, at intermediate lengthscales, on the nonfrustrated square lattice as well.

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• Cold gases in optical lattices
• Ferromagnetism
• Frustrated magnetism
• Ultracold gases
• Hubbard model