**Quadratic scaling bosonic path integral molecular dynamics**

YMY Feldman and B Hirshberg, JOURNAL OF CHEMICAL PHYSICS, 159, 154107 (2023).

DOI: 10.1063/5.0173749

Bosonic exchange symmetry leads to fascinating quantum phenomena, from exciton condensation in quantum materials to the superfluidity of liquid He-4. Unfortunately, path integral molecular dynamics (PIMD) simulations of bosons are computationally prohibitive beyond similar to 100 particles, due to a cubic scaling with the system size. We present an algorithm that reduces the complexity from cubic to quadratic, allowing the first simulations of thousands of bosons using PIMD. Our method is orders of magnitude faster, with a speedup that scales linearly with the number of particles and the number of imaginary time slices (beads). Simulations that would have otherwise taken decades can now be done in days. In practice, the new algorithm eliminates most of the added computational cost of including bosonic exchange effects, making them almost as accessible as PIMD simulations of distinguishable particles. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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