Path integral Monte Carlo simulation of degenerate electrons: Permutation-cycle properties

Area of Science:

• Computational Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Fermionic quantum Monte Carlo simulations are increasingly used at finite temperatures.
• Understanding the behavior of degenerate electrons in systems like warm dense matter is crucial.

Purpose of the Study:

• To analyze the permutation-cycle properties of path integral Monte Carlo (PIMC) simulations for degenerate electrons.
• To investigate the impact of finite-size effects on these properties in uniform electron gas and inhomogeneous systems.

Main Methods:

• Path Integral Monte Carlo (PIMC) simulations were performed for up to 100 electrons.
• Exchange-cycle frequencies and a novel permutation-cycle correlation function were analyzed.

Main Results:

• Exchange-cycle frequencies do not follow simple exponential laws due to finite-size effects.
• Finite-size effects were also found to predominate in the analysis of permutation-cycle correlations.
• Behavior was studied in uniform electron gas and a 2D harmonic trap.

Conclusions:

• Finite-size effects are a dominant factor in PIMC simulations of degenerate electrons.
• The developed permutation-cycle correlation function provides insights into cycle distributions.
• Results are expected to aid in developing fermionic PIMC methods and mitigating the fermion sign problem.