Periodic Boundary Conditions for Bosonic Path Integral Molecular Dynamics
arXiv:2501.17618 · doi:10.1063/5.0265906
Abstract
We develop an algorithm for bosonic path integral molecular dynamics (PIMD) simulations with periodic boundary conditions (PBC) that scales quadratically with the number of particles. Path integral methods are a powerful tool to simulate bosonic condensed phases, which exhibit fundamental physical phenomena such as Bose--Einstein condensation and superfluidity. Recently, we developed a quadratic scaling algorithm for bosonic PIMD, but employed an ad hoc treatment of PBC. Here we rigorously enforce PBC in bosonic PIMD. It requires summing over the spring energies of all periodic images in the partition function, and a naive implementation scales exponentially with the system size. We present an algorithm for bosonic PIMD simulations of periodic systems that scales only quadratically. We benchmark our implementation on the free Bose gas and a model system of cold atoms in optical lattices. We also study an approximate treatment of PBC based on the minimum-image convention, and derive a numerical criterion to determine when it is valid.
References in corpus (10)
- Nuclear quantum effects enter the mainstream
- Path Integral Molecular Dynamics for Bosons
- Path Integral Molecular Dynamics for Fermions: Alleviating the Sign Problem with the Bogoliubov Inequality
- Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
- On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
- Prediction of a supersolid phase in high-pressure deuterium
- Path-integral Monte Carlo worm algorithm for Bose systems with periodic boundary conditions
- Quadratic Scaling Bosonic Path Integral Molecular Dynamics
- Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
- Path integral molecular dynamics simulations for Green's function in a system of identical bosons