Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

Area of Science:

• Computational Physics
• Materials Science
• Quantum Mechanics

Background:

• Fermionic path integral Monte Carlo (FPIMC) simulations are crucial for understanding matter under extreme conditions.
• Extending FPIMC to heavier elements and lower temperatures presents significant computational challenges.
• Accurate equations of state are vital for modeling dense plasmas and warm dense matter.

Purpose of the Study:

• To enhance the applicability of FPIMC simulations for heavier elements and lower temperatures.
• To develop a consistent equation of state for hot, dense silicon.
• To characterize the fluid structure of silicon under extreme conditions.

Main Methods:

• Introduction of various localized nodal surfaces within FPIMC simulations.
• Utilizing Hartree-Fock nodes for accurate prediction of pressure and internal energy.
• Combining FPIMC results with density functional molecular dynamics simulations.
• Derivation of the shock Hugoniot curve and analysis of pair correlation functions.

Main Results:

• Successfully extended FPIMC applicability to heavier elements and lower temperatures.
• Hartree-Fock nodes provided accurate predictions for pressure and internal energy.
• A consistent equation of state for hot, dense silicon was obtained.
• Characterized the fluid structure using pair correlation functions.

Conclusions:

• The developed method significantly advances the capabilities of FPIMC simulations for condensed matter physics.
• The equation of state for silicon is applicable to plasma and warm dense matter regimes.
• This work provides a foundation for future studies on the properties of dense materials.