Accelerated Free Energy Estimation in Ab Initio Path Integral Monte Carlo Simulations

Area of Science:

• Computational Physics
• Quantum Many-Body Systems

Background:

• Path integral Monte Carlo (PIMC) simulations are crucial for understanding quantum systems.
• Estimating free energy in PIMC can be computationally intensive, limiting system size and accuracy.

Purpose of the Study:

• To develop a methodology for accelerating free energy calculations in PIMC simulations.
• To address the computational cost and the Fermion sign problem in quantum electron gas simulations.

Main Methods:

• An intermediate artificial reference system (spherically averaged Ewald interaction) was employed.
• An extrapolation technique was used to mitigate the Fermion sign problem.
• The method was applied to a uniform electron gas system.

Main Results:

• Free energy calculations were accelerated up to 18 times compared to the Ewald-only method.
• Finite-size and statistical errors were reduced below chemical accuracy for a system of 1000 electrons.
• The combined techniques successfully alleviated the Fermion sign problem.

Conclusions:

• The presented methodology significantly enhances the efficiency of free energy estimation in PIMC.
• This approach is applicable to quantum systems relevant in planetary and fusion modeling.
• Accurate simulations of quantum degenerate systems are now more feasible.