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We show that, by an appropriate choice of auxiliary fields and exactintegration of the phonon degrees of freedom, it is possible to define a'sign-free' path integral for the so called Hubbard-Holstein model athalf-filling. We use a statistical method, based on an accelerated andefficient Langevin dynamics, for evaluating all relevant correlation functionsof the model. Preliminary calculations at $U/t=4$ and $U/t=1$, for$\omega_0/t=1$, indicate a quite extended region around $U \simeq {g^2 \over\omega_0}$ without either antiferromagnetic or charge-density-wave orders,separating two quantum critical points at zero temperature. The elimination ofthe sign problem in a model without explicit particle-hole symmetry may opennew perspectives for strongly correlated models, even away from the purelyattractive or particle-hole symmetric cases.

Solution of the "sign problem" for the half filled Hubbard-Holstein model