Ferromagnetism in Correlated Electron Systems: Generalization of Nagaoka's Theorem

Marcus Kollar; Rainer Strack; Dieter~Vollhardt

doi:10.1103/PhysRevB.53.9225

paper

Ferromagnetism in Correlated Electron Systems: Generalization of Nagaoka's Theorem

arXiv:cond-mat/9511060 · doi:10.1103/PhysRevB.53.9225

Abstract

Nagaoka's theorem on ferromagnetism in the Hubbard model with one electron less than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions (the density-density interaction $V$ , bond-charge interaction $X$ , exchange interaction $F$ , and hopping of double occupancies $F^{'}$ ) are included. It is shown that for ferromagnetic exchange coupling ( $F > 0$ ) ground states with maximum spin are stable already at finite Hubbard interaction $U > U_{c}$ . For non-bipartite lattices this requires a hopping amplitude $t \leq 0$ . For vanishing $F$ one obtains $U_{c} \to \infty$ as in Nagaoka's theorem. This shows that the exchange interaction $F$ is important for stabilizing ferromagnetism at finite $U$ . Only in the special case $X = t$ the ferromagnetic state is stable even for $F = 0$ , provided the lattice allows the hole to move around loops.

13 pages, uuencoded postscript, includes 1 table and 2 figures

Ferromagnetism in Correlated Electron Systems: Generalization of Nagaoka's Theorem

Abstract

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