A staging Monte Carlo algorithm for sampling off-diagonal density matrix elements via open-chain path integrals

Area of Science:

• Computational physics
• Quantum mechanics

Background:

• Imaginary-time Feynman path integration is crucial for quantum system simulations.
• Existing methods for sampling polymer-like chains can be computationally intensive.

Purpose of the Study:

• To introduce a computationally simple algorithm for sampling open-chain distributions.
• To enable efficient calculation of momentum-dependent quantities in quantum systems.

Main Methods:

• The staging open path integral Monte Carlo (OPIMC) algorithm samples off-diagonal density matrix elements.
• It utilizes a staging transformation to sample polymer-like chains from a free-particle distribution.
• The method involves sampling Gaussian distributions and a Metropolis acceptance/rejection step.

Main Results:

• The staging OPIMC method accurately reproduces end-to-end distributions.
• It also accurately reproduces momentum distributions for various quantum systems.
• The algorithm was validated on systems from coupled harmonic oscillators to liquid water.

Conclusions:

• The staging OPIMC algorithm provides a computationally simple and efficient approach.
• It is effective for simulating quantum systems and calculating key distributions.
• The method is straightforward to implement for researchers in computational physics.