### Abstract

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 finite lattice). The phonons interact with the electronic system in two different 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 of a finite system 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 finite 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-Schrieffer-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 dimensionseven on a general graph without periodic lattice structure.

Original language | English (US) |
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Pages (from-to) | 2812-2821 |

Number of pages | 10 |

Journal | Physical Review B |

Volume | 51 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1995 |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

*51*(5), 2812-2821. https://doi.org/10.1103/PhysRevB.51.2812