 94223 Lieb E. H. , Freericks J. K.
 THE GROUND STATE OF A GENERAL ELECTRONPHONON HAMILTONIAN IS A SPIN SINGLET
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Jul 2, 94

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Abstract. The manybody ground state of a very general class of
electronphonon 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 waysthere 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 electronphonon couplings and the hopping matrix elements may
be nonlinear functions of the phonon coordinates. 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
groundstate level crossings, and that the groundstate energy is an
analytic function of the parameters in the Hamiltonian. In particular,
in a finite system any selftrapping transition is a smooth crossover
not accompanied by a nonanalytical change in the ground state. The
spinsinglet theorem applies to the SuSchriefferHeeger model and both
the spinsinglet 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.
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