Ferromagnetism in doped Hubbard models in optical lattices

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. Here, we study a variant of such a model wherein any second electron on a single lattice site is weakly bound compared to the first¹. Employing large-scale density-matrix renormalization group and exact diagonalization calculations in both one and two spatial dimensions, we establish the existence of high-spin ground states on the nanoscale, study their subtle interplay with lattice geometries, and investigate the competition between ferromagnetic and stripe orders. We also discuss the experimental realization of this system in current-generation optical lattice platforms via the careful use of Feshbach resonances.



¹Erik Nielsen and R. N. Bhatt, Physical Review B 76, 161202(R) (2007); Physical Review B 82, 195117 (2010).