arXiv:1008.2056v3 Announce Type: replace Abstract: We study a finite Hubbard model coupled to a massless phonon field through a form factor common to all sites that satisfies the infrared singular condition. The Hamiltonian has no ground state in the Fock representation. With the unitary transformation of Arai and Hirokawa, the ground states with infrared cutoff define states on the Weyl algebra over the form domain of the inverse dispersion, and they converge to a ground state in a representation inequivalent to the Fock representation. In this representation the ground states are the products of the ground states of the Hubbard model and the phonon vacuum, so that the model has ferromagnetic or unique spin-singlet ground states according to the hopping matrix and the electron number.
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