Combining harmonic sampling with the worm algorithm to improve the efficiency of path integral Monte Carlo.

Area of Science:

• Quantum Many-Body Physics
• Computational Physics

Background:

• Path Integral Monte Carlo (PIMC) is crucial for quantum condensed phases.
• Standard PIMC faces challenges with low acceptance ratios in solids and dense liquids.

Purpose of the Study:

• To develop improved PIMC algorithms (H-PIMC and M-PIMC) for enhanced efficiency.
• To address sampling limitations in solids and dense confined liquids.

Main Methods:

• Developed H-PIMC: exact sampling of harmonic potential contributions, acceptance based on anharmonic part.
• Developed M-PIMC: restricted harmonic sampling near minima, standard PIMC elsewhere.
• Combined H-PIMC/M-PIMC with the worm algorithm for indistinguishable particles.

Main Results:

• H-PIMC significantly improves acceptance ratios (6-16x) and reduces autocorrelation times (7-30x) for weakly to moderately anharmonic systems.
• H-PIMC achieves faster convergence, reducing required imaginary time slices by 2-3x.
• M-PIMC optimizes autocorrelation time for strongly anharmonic systems and periodic potentials.

Conclusions:

• H-PIMC and M-PIMC offer substantial efficiency gains for PIMC simulations.
• These methods effectively overcome sampling limitations in challenging condensed matter systems.
• Integration with the worm algorithm extends benefits to systems of indistinguishable particles.