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We study the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model onthe square lattice by using a novel variational wave function. Taking the cluefrom the backflow correlations that have been introduced long-time ago byFeynman and Cohen and have been used for describing various interacting systemson the continuum (like liquid $^3$He, the electron jellium, and metallicHydrogen), we consider many-body correlations to construct a suitableapproximation for the ground state of this correlated model on the lattice. Inthis way, a very accurate {\it ansatz} can be achieved both at weak and strongcoupling. We present the evidence that an insulating and non-magnetic phase canbe stabilized at strong coupling and sufficiently large frustrating ratio$t^\prime/t$.

Metal-insulator transition and strong-coupling spin liquid in the $t{-}t^\prime$ Hubbard model