We propose a method to construct the ground state ψ(λ) of local
lattice hamiltonians with the generic form H0+λH1, where λ
is a coupling constant and H0 is a hamiltonian with a non degenerate ground
state ψ0. The method is based on the choice of an exponential ansatz
ψ(λ)=exp(U(λ))ψ0, which is a sort of generalized
lattice version of a Jastrow wave function. We combine perturbative and
variational techniques to get succesive approximations of the operator
U(λ). Perturbation theory is used to set up a variational method which
in turn produces non perturbative results. The computation with this kind of
ansatzs leads to associate to the original quantum mechanical problem a
statistical mechanical system defined in the same spatial dimension. In some
cases these statistical mechanical systems turn out to be integrable, which
allow us to obtain exact upper bounds to the energy. The general ideas of our
method are illustrated in the example of the Ising model in a transverse field.Comment: 27 pages, three .ps figures appended, DFTUZ 94-2