Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States

We develop a new projected wave function approach which is based on projection operators in the form of matrix-product operators (MPOs). Our approach allows to variationally improve the short range entanglement of a given trial wave function by optimizing the matrix elements of the MPOs while the long range entanglement is contained in the initial guess of the wave function. The optimization is performed using standard variational Monte Carlo techniques. We demonstrate the efficiency of our approach by considering a one-dimension model of interacting spinless fermions. In addition, we indicate how to generalize this approach to higher dimensions using projection operators which are based on tensor products.