Fermionic shadow wave function variational calculations of the vacancy formation energy in 3He

Area of Science:

• Quantum Many-Body Physics
• Condensed Matter Physics

Background:

• Studying the ground state of inhomogeneous fermionic matter is crucial for understanding various quantum systems.
• Existing methods face challenges, particularly the sign problem, when dealing with complex systems like those with defects or impurities.

Purpose of the Study:

• To introduce a novel fermionic shadow wave function technique for analyzing the ground state of inhomogeneous fermionic matter.
• To demonstrate the applicability of this method in systems with coexisting phases, defects, or impurities.

Main Methods:

• The system is modeled using a fermionic shadow wave function.
• Energy is computed via the variational Monte Carlo technique.
• The method is designed to address the significant sign problem inherent in such systems.

Main Results:

• The fermionic shadow wave function proves effective for describing many-body systems with complex characteristics.
• The variational Monte Carlo approach successfully computes the ground state energy.
• The study successfully applied the technique to calculate the energy required to activate vacancies in solid Helium-3 (3He).

Conclusions:

• The presented fermionic shadow wave function technique offers a powerful new tool for studying inhomogeneous fermionic matter.
• This method provides a viable approach to overcome the sign problem in complex quantum systems.
• The application to solid 3He demonstrates the practical utility of the technique for condensed matter research.