Fermionic Shadow Wave Function Variational Calculations of the Vacancy Formation Energy in ${}^3\mathrm{He}$

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 ${}^3\mathrm{He}$.

Figure 1

The FSWF energy per particle (black circles) as a function of the density. The result is compared with the two results provided by the ASWF of Ref. 7 (blue triangles and red diamonds) and with the DMC results of Ref. 12 (green squares).

Figure 2

The vacancy-formation energy $\Delta E_v$ as a function of the density using the FSWF (black circles) and by keeping the shadows fixed. Some experimental data from Ref. 17 is also reported for comparison. See the text for details.