fix pimd/langevin: An efficient implementation of path integral molecular dynamics in LAMMPS

Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are, therefore, computationally demanding. While software packages such as i-PI offer comprehensive PIMD functionality, the high efficiency of simulations driven by machine learning interatomic potentials, such as deep potential (DP), calls for more efficient PIMD implementations that fully exploit modern massively parallel supercomputers. Here, we present fix pimd/langevin, an efficient PIMD implementation in LAMMPS that supports commonly used features and leverages the Message Passing Interface architecture of LAMMPS to achieve high computational efficiency. We demonstrate the usage, validate the correctness of our code using liquid water as a representative example, and provide a comprehensive overview of the supported features. Then, we discuss several important technical aspects of the implementation. Using DP simulations of water as a benchmark, we show that our implementation achieves several-fold acceleration compared to i-PI. Finally, we report strong and weak scaling results that demonstrate the favorable parallel performance of our code.