Path integral molecular dynamics for bosons

Barak Hirshberg, Valerio Rizzi, Michele Parrinello

Research output: Contribution to journalArticlepeer-review


Trapped bosons exhibit fundamental physical phenomena and are at the core of emerging quantum technologies. We present a method for simulating bosons using path integral molecular dynamics. The main difficulty in performing such simulations is enumerating all ring-polymer configurations, which arise due to permutations of identical particles. We show that the potential and forces at each time step can be evaluated by using a recurrence relation which avoids enumerating all permutations, while providing the correct thermal expectation values. The resulting algorithm scales cubically with system size. The method is tested and applied to bosons in a 2-dimensional (2D) trap and agrees with analytical results and numerical diagonalization of the many-body Hamiltonian. An analysis of the role of exchange effects at different temperatures, through the relative probability of different ring-polymer configurations, is also presented.

Original languageEnglish
Pages (from-to)21445-21449
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number43
StatePublished - 22 Oct 2019
Externally publishedYes


  • Bosons
  • Cold atoms
  • Molecular dynamics
  • Path integrals


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