Path integral molecular dynamics for bosons

Abstract

Significance Path integral molecular dynamics (PIMD) simulations are widely used to describe nuclear quantum effects in chemistry and physics. However, they neglect exchange symmetry, a fundamental property of quantum systems, since it is impossible to enumerate all permutations of identical particles for large systems. We develop a method for performing PIMD simulations for bosons by showing that the potential energy and forces can be evaluated recursively without the need to enumerate all permutations. The resulting approach scales cubically with system size, allowing performing PIMD simulations for large bosonic systems. We apply the method to study trapped cold atoms, which play a key role in emerging quantum technologies and exhibit fundamental physical phenomena. 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.