  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.
