Absence of phase transitions in Holstein systems

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Abstract
We consider a model of a particle, which is positioned at fixed discrete-lattice sites and interacts with the phonons of the lattice, described by a generalized Holstein Hamiltonian. As physically interesting situations, the molecular polaron, the Frenkel-exciton–phonon system in molecular aggregates, and the small polaron in a crystal are included. We prove that, for optical-phonon dispersions, there is no abrupt (nonanalytical) phase transition of the ground state as the phonon coupling increases. This result holds for both finite-N-site models and infinite-site models. For nonzero temperature, the free energy is smooth for arbitrary phonon dispersions. Furthermore, we show that the ground-state wave function of a small polaron is delocalized for any coupling strength. As a consequence, the self-trapping transition is a smooth crossover which is not accompanied by a localization transition or a nonanalytical change of the ground state.