Periodic boundary conditions for bosonic path integral molecular dynamics
Jacob Higer1, Yotam M Y Feldman2, Barak Hirshberg2,3,4
1School of Physics, Tel Aviv University, Tel Aviv 6997801, Israel.
The Journal of Chemical Physics
|July 8, 2025
Summary
We developed a new algorithm for simulating bosonic condensed phases using path integral molecular dynamics (PIMD) with periodic boundary conditions (PBC). This method efficiently handles periodic systems, enabling accurate simulations of quantum phenomena like superfluidity.
Area of Science:
- Computational physics
- Quantum mechanics
- Condensed matter physics
Background:
- Path integral methods are crucial for simulating bosonic condensed phases.
- These phases exhibit phenomena like Bose-Einstein condensation and superfluidity.
- Previous quadratic-scaling algorithms for bosonic PIMD lacked rigorous treatment of periodic boundary conditions (PBC).
Purpose of the Study:
- To develop and rigorously implement an algorithm for bosonic path integral molecular dynamics (PIMD) simulations that correctly handles periodic boundary conditions (PBC).
- To ensure the algorithm scales quadratically with system size, improving computational efficiency for large systems.
Main Methods:
- Developed a novel algorithm for bosonic PIMD that rigorously incorporates PBC.
- Implemented a method to sum over spring energies of all periodic images in the partition function.
- Analyzed the computational scaling, achieving quadratic complexity.
Main Results:
- Successfully implemented a quadratic-scaling algorithm for bosonic PIMD with rigorous PBC.
- Benchmarked the algorithm on a free Bose gas and cold atoms in optical lattices.
- Investigated an approximate PBC treatment using the minimum-image convention and established a validity criterion.
Conclusions:
- The new algorithm provides an efficient and accurate method for simulating bosonic condensed phases with PBC.
- This advancement enables more reliable studies of quantum phenomena in periodic systems.
- The derived criterion for the minimum-image convention aids in selecting appropriate simulation approximations.
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