Lattice dependence of saturated ferromagnetism in the Hubbard model

Physics – Condensed Matter – Strongly Correlated Electrons

Scientific paper

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Revtex, 18 pages with 18 figures, 7 pages appendices, section on bcc lattice added

Scientific paper

10.1103/PhysRevB.56.13960

We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2 and d=3. A variational resolvent approach is developed for the Nagaoka instability both for U = infinity and for U < infinity which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low density limit.

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