Ground state of a general electron-phonon Hamiltonian is a spin singlet.

The many-body ground state of a very general class of electron-phonon Hamiltonians is proven to contain a spin singlet (for an even number of electrons on a nite lattice). The phonons interact with the electronic system in two diierent ways|there is an interaction with the local electronic charge and there is a functional dependence of the electronic hopping Hamiltonian on the phonon coordinates. The phonon potential energy may include anharmonic terms, and the electron-phonon couplings and the hopping matrix elements may be nonlinear functions of the phonon coordinates. An attractive Hubbard type on-site interaction may also be added. If the hopping Hamiltonian is assumed to have no phonon coordinate dependence, then the ground state is also shown to be unique, implying that there are no ground-state level crossings, and that the ground-state energy is an analytic function of the parameters in the Hamiltonian. In particular, in a nite system any self-trapping transition is a smooth crossover not accompanied by a nonanalytical change in the ground state. The spin-singlet theorem applies to the Su-Schrieeer-Heeger model and both the spin-singlet and uniqueness theorems apply to the Holstein and attractive Hubbard models as special cases. These results hold in all dimensions | even on a general graph without periodic lattice structure. 1994 by the authors. Reproduction of this article by any means is permitted for non-commercial purposes.