Stability of ferromagnetism in Hubbard models with degenerate single-particle ground states

Abstract

A Hubbard model with a Nd-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less than or equal to Nd. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: the model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to Nd , it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result.