EFFECTIVE ACTION AND ADIABATIC EXPANSIONS FOR THE 1-D AND 2-D HUBBARDMODELS AT HALF-FILLING

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions usin g a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly alr eady at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry's phase c ontributions arise quite naturally from the adiabatic expansion. At lo w temperatures and in the continuum limit the model gets mapped onto a n O(3) nonlinear sigma model (NLsigma). A topological, Wess-Zumino ter m is present in the effective action of the ID NLsigma as expected, wh ile no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expa nsion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.