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.

翻译：基于路径积分的平均场分子动力学用于近似由原子核和电子组成的粒子系统的量子典范观测量。计算瓶颈在于从电子算符的吉布斯密度中进行采样，由于费米子符号问题，其计算复杂度随电子数量呈指数增长。本研究构建了一种算法，通过费米子路径积分近似平均场哈密顿量。该算法基于一个矩阵的行列式，其分量由连接置换电子坐标的布朗桥构成。对于$n$个电子，计算工作量为$\mathcal O(n^3)$，这降低了与费米子符号问题相关的计算复杂度。我们分析了该近似产生的偏差，并提供了计算误差指标。至于其异常高的精度，仍有待严格解释。