A multi-projective variational approach to the quantum lattice problem

We formulate a general method for constructing a variational expression of the total energy based on two projective ansatz from the weak and strong coupling limits. These two ansatz are then combined according to individual and mutual interactions of low and high energy degrees of freedom. We apply our approach to the single band Hubbar model, where the theory yields the double occupancy and the nonlocal single-particle density matrix. We compare to exact results for d=1 and d=infinity. For d=1, the insulating state is properly obtained at infinitesimal u; in addition to an accurate prediction of the ground state energy over a broad range of t/U. In infinite dimensions, we properly find a finite-U metal-insulator transition with reasonable quantitative accuraccy across all parameter space. Our approach has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context of total energies for strongly correlated materials and molecules.