Harmonic Oscillator Staging Coordinates for Efficient Path Integral Simulations of Quantum Oscillators and Crystals

Area of Science:

• Quantum Mechanics
• Computational Physics
• Statistical Mechanics

Background:

• Imaginary-time path integral (PI) is crucial for finite-temperature quantum mechanics.
• Sampling challenges arise from stiff PI modes, often addressed with free particle (FP) staging coordinates.
• FP staging diagonalizes only the free particle contribution to the PI action.

Purpose of the Study:

• Introduce novel harmonic oscillator (HO) staging coordinates to diagonalize the entire action for harmonic systems.
• Enhance sampling efficiency in path integral Monte Carlo (PIMC) and path integral molecular dynamics (PIMD) simulations.
• Improve accuracy and precision in calculating static properties of quantum oscillators and crystals.

Main Methods:

• Developed HO staging coordinates that diagonalize the full harmonic oscillator action.
• Implemented HO staging in PIMC and PIMD simulations within the NVT ensemble.
• Assessed sampling efficiency using energy and heat capacity calculations for 1D HO and anharmonic oscillator models.

Main Results:

• HO staging provides superior sampling efficiency and accuracy compared to FP staging for harmonic systems.
• HO staging uniquely treats the centroid mode and allows larger time steps in PIMD.
• PIMC with HO staging achieves high acceptance rates and precision for anharmonic potentials.

Conclusions:

• HO staging coordinates offer a computationally efficient and accurate method for systems with harmonic character.
• This approach is particularly beneficial for simulating nuclear quantum effects in molecular bonds and quantum crystals.
• The method provides a significant advancement over traditional FP staging and normal mode approaches.