2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/18271A variational approach is proposed to determine some properties of the adiabatic Holstein-Hubbard model which describes the interactions between a static atomic lattice and an assembly of fermionic charge carriers. The sum of the electronic energy and the lattice elastic energy is proved to have minima with a polaron structure in a certain domain of the phase diagram. Our analytical work consists in the expansion of these energy minima from the zero electronic transfer limit which remarkably holds for a finite amplitude of the onsite Hubbard repulsion and for an unbounded lattice size.submitted to Journal of Statistical PhysicsStrongly Correlated ElectronsSuperconductivitytext