Fermionic Shadow Wave Function Variational Calculations of the Vacancy Formation Energy in ³He

We present a novel technique well suited for studying the ground state of inhomogeneous fermionic matter in a wide range of different systems. The system is described using a fermionic shadow wave function, and the energy is computed by means of the variational Monte Carlo technique. The general form of the fermionic shadow wave function is useful for describing 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 ³He.