Stability of ferromagnetism in many-electron systems

TL;DR

This paper develops a model-independent operator-theoretic framework to analyze the stability of ferromagnetism in strongly correlated electron systems, extending classical theorems to more complex interactions.

Contribution

It introduces a novel, general framework for ferromagnetism stability analysis and reinterprets key theorems, including their validity with additional interactions.

Findings

Reinterpretation of the Marshall-Lieb-Mattis and Lieb's theorems

Proof that Lieb's theorem holds with electron-phonon and electron-photon interactions

Verification of the stability of Nagaoka-Thouless theorem

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\rq{}s theorem; in addition, from the new perspective, we prove that Lieb\rq{}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.