Stability of Ferromagnetism in Many-Electron Systems

Abstract

We construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems; Our description relies on the operator theoretic correlation inequalities. Within the new framework, we reinterpret the Marshall–Lieb–Mattis theorem and Lieb’s theorem; in addition, from the new perspective, we prove that Lieb’s theorem still holds true even if the electron–phonon and electron–photon interactions are taken into account. We also examine the Nagaoka–Thouless theorem and its stabilities. These examples verify the effectiveness of our new viewpoint.