Restricted configuration path integral Monte Carlo

Area of Science:

• Computational Physics
• Quantum Many-Body Systems
• Quantum Plasma Simulations

Background:

• Quantum Monte Carlo (QMC) is a highly accurate simulation method for quantum many-particle systems.
• The fermion sign problem limits traditional QMC simulations in strongly degenerate regimes.
• Configuration Path Integral Monte Carlo (CPIMC) enabled ab initio simulations for dense quantum plasmas but faces a complementary sign problem at lower densities.

Purpose of the Study:

• To extend the applicability of CPIMC to lower densities (stronger coupling) by introducing restricted versions.
• To investigate the accuracy and feasibility of these new restricted CPIMC methods.
• To determine the optimal parameter ranges for accurate ab initio simulations of quantum plasmas.

Main Methods:

• Introduction of two restricted CPIMC variants: RCPIMC and RCPIMC+.
• These methods omit specific sign-changing Monte Carlo updates to mitigate the sign problem.
• Extensive simulations of the ferromagnetic uniform electron gas were performed.

Main Results:

• RCPIMC completely eliminates the sign problem but introduces systematic errors.
• RCPIMC+ offers a more accurate approach by neglecting a smaller subset of Monte Carlo steps.
• Both methods are effective at temperatures Θ ≈ 0.1–0.5, enabling simulations with density parameters up to r_s ≈ 3–5.

Conclusions:

• Restricted CPIMC methods (RCPIMC and RCPIMC+) partially bridge the gap left by traditional QMC methods.
• These new techniques significantly extend the accessible parameter range for ab initio simulations of quantum plasmas.
• RCPIMC+ provides a feasible and accurate approach for studying strongly coupled quantum systems.