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

TL;DR

This paper introduces a Fermionic Shadow Wavefunction (FSWF) method combined with Variational Monte Carlo to study inhomogeneous fermionic systems, specifically calculating vacancy formation energy in solid $^3$He, addressing the sign problem.

Contribution

The paper presents a novel FSWF approach for inhomogeneous fermionic matter, enabling accurate energy calculations despite the sign problem, applied to vacancy formation in $^3$He.

Findings

Successfully computed vacancy formation energy in solid $^3$He.

Demonstrated FSWF's effectiveness in handling inhomogeneous fermionic systems.

Addressed the sign problem in fermionic Monte Carlo simulations.

Abstract

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.