The Lieb--Thomas strategy for strongly coupled fermionic multipolarons with general external fields

Abstract

In this article, we prove that the ground-state energy of a fermionic Fr\"ohlich multipolaron can be approximated, in the strong electron-phonon coupling limit, by the ground-state energy of a corresponding fermionic Pekar-Tomasevich multipolaron, even in the presence of external electric and magnetic fields. Our analysis builds upon Lieb and Thomas' approach \cite{liebthomas}, which was originally developed for a single polaron without external fields, and Wellig's generalization to multipolarons \cite{wellig} with (specialized) external fields. Our main new contributions are twofold. First, we take into account the fermionic statistics of the multipolaron by employing a localization method from \cite{liebloss}. Second, we relax an assumption in \cite{wellig} on the external electric and magnetic fields, which is not easily verifiable unless the fields are periodic. Instead, we allow for general fields that only ensure self-adjointness of the Fr\"ohlich Hamiltonian. In particular, our work demonstrates the robustness of the Lieb--Thomas strategy when extended to fermionic multipolarons and general external potentials.