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We introduce an efficient way to improve the accuracy of projected wavefunctions, widely used to study the two-dimensional Hubbard model. Taking theclue from the backflow contribution, whose relevance has been emphasized forvarious interacting systems on the continuum, we consider many-bodycorrelations to construct a suitable approximation for the ground state atintermediate and strong couplings. In particular, we study the phase diagram ofthe frustrated $t{-}t^\prime$ Hubbard model on the square lattice and showthat, thanks to backflow correlations, an insulating and non-magnetic phase canbe stabilized at strong coupling and sufficiently large frustrating ratio$t^\prime/t$.

Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model