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arXiv · 2311.17333

Path integral molecular dynamics approximations of quantum canonical observables

Xin Huang·Petr Plechac·Mattias Sandberg·Anders Szepessy
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Abstract

Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the electron operator, which due to the fermion sign problem has a computational complexity that scales exponentially with the number of electrons. In this work we construct an algorithm that approximates the mean-field Hamiltonian by path integrals for fermions. The algorithm is based on the determinant of a matrix with components based on Brownian bridges connecting permuted electron coordinates. The computational work for $n$ electrons is $\mathcal O(n^3)$, which reduces the computational complexity associated with the fermion sign problem. We analyze a bias resulting from this approximation and provide a computational error indicator. It remains to rigorously explain the surprisingly high accuracy.

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Xin Huang, Petr Plechac, Mattias Sandberg, Anders Szepessy. 2023-11-29. Path integral molecular dynamics approximations of quantum canonical observables. https://arxiv.org/abs/2311.17333

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