Fermionic Shadow Wavefunction Variational calculations of the vacancy formation energy in ³He

We present a novel technique well suited to study the ground state of inhomogeneous fermionic matter in a wide range of different systems. The system is described using a Fermionic Shadow wavefunction (FSWF) and the energy is computed by means of the Variational Monte Carlo technique. The general form of FSWF is useful to describe many--body systems with the coexistence of different phases as well in the presence of defects or impurities, but it requires overcoming a significant sign problem. As an application, we studied the energy to activate vacancies in solid $^3$He.