GPU acceleration for simulations of large-scale identical particles based on path integral molecular dynamics

In this work, we achieved significant GPU acceleration based on quadratic scaling path integral molecular dynamics (PIMD) [Feldman and Hirshberg, J. Chem. Phys. 159, 154107 (2023)] and developed an open-source PIMD code repository. Numerical experiments show that for a system of 1600 interacting identical bosons in a harmonic trap, using a single GPU and a single CPU, it only takes two hours to achieve satisfactory simulation accuracy. With the increase in the number of identical particles, the advantage of GPU acceleration over CPU becomes more obvious, making it possible to simulate tens of thousands of identical particles from first principles using a single GPU. Our study shows that GPU acceleration can lay a solid foundation for the wide application of PIMD simulations for large-scale identical particle quantum systems with more than 10 000 particles in the presence of two-body interaction. Numerical experiments show that a 24 GB GPU can simulate up to 20 000 identical particles from first principles, and the GPU acceleration leads to a roughly linear relationship between the computation time and the number of identical particles. In addition, we have also successfully implemented simulations for fictitious identical particle thermodynamics using GPU to overcome the fermion sign problem, which makes it promising to efficiently and accurately simulate tens of thousands of fermions based on GPU when the recently proposed ξ-extrapolation method holds.