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

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

1995-11-13

arxiv.org/abs/cond-mat/9511060v1

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevB.53.9225

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 $t\leq0$. 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.

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