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The search for ferromagnetism in the Hubbard model has been a problem ofoutstanding interest since Nagaoka's original proposal in 1966. Recent advancesin quantum simulation have today enabled the study of tunable doped Hubbardmodels in ultracold atomic systems. Here, we examine a realistic variant ofsuch a model wherein any second electron on a single lattice site is weaklybound compared to the first one. Employing large-scale density-matrixrenormalization group calculations, we establish the existence of high-spinground states on square and triangular lattices, analyze the microscopicmechanisms behind their origin, and investigate the interplay betweenferromagnetism and other competing orders, such as stripes. Our results alsoexplain$\unicode{x2014}$and shed new light on$\unicode{x2014}$the intriguingobservations of ferromagnetic correlations in recent optical-latticeexperiments.

Nagaoka ferromagnetism in doped Hubbard models in optical lattices