We define a numerical scheme that allows to approximate a given Hamiltonian
by an effective one, by requiring several constraints determined by exact
properties of generic ''short range'' Hamiltonians. In this way the standard
lattice fixed node is also improved as far as the variational energy is
concerned. The effective Hamiltonian is defined in terms of a guiding function
ψG and can be solved exactly by Quantum Monte Carlo methods. We argue
that, for reasonable ψG and away from phase transitions, the long
distance, low energy properties are rather independent on the chosen guiding
function, thus allowing to remove the well known problem of standard
variational Monte Carlo schemes based only on total energy minimizations, and
therefore insensitive to long distance low energy properties.Comment: 8 pages, for the proceedings of "The Monte Carlo Method in the
Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200