 VMC is no different from any other variational method, except that the many-dimensional integrals are evaluated numerically.Monte Carlo integration is particularly crucial in this problem since the dimension of the many-body Hilbert space, comprising all the possible values of the configurations formula_5, typically grows exponentially with the size of the physical system.Other approaches to the numerical evaluation of the energy expectation values would therefore, in general, limit applications to much smaller systems than those analyzable thanks to the Monte Carlo approach.