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

TL;DR

This paper rigorously proves that in Hubbard models with degenerate ground states, local stability of ferromagnetism guarantees global stability, and it clarifies conditions for the uniqueness of ferromagnetic ground states.

Contribution

It establishes a rigorous link between local and global stability of ferromagnetism in degenerate Hubbard models and simplifies the proof of the uniqueness condition.

Findings

Local stability implies global stability of ferromagnetism.

Ferromagnetic ground states are unique iff the single-particle density matrix is irreducible.

Simplified proof of the uniqueness condition for ferromagnetic ground states.

Abstract

A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. 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 N_d, 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.