Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

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Abstract

We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δcr = 0.407 for the SKA spin wave and of δcr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.

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