路径积分蒙特卡罗模拟中的费米子符号问题：量子点、超冷原子和热稠密物质
The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
摘要：
关联费米体系的从头算热力学模拟在热的致密物质、量子点中的电子和超冷原子等许多应用中具有重要意义。不幸的是，费米子的路径积分蒙特卡罗（PIMC）模拟受到著名的费米子符号问题（FSP）的严重限制。在这项工作中，我们提出了一个动手讨论的FSP和详细调查其表现形式的温度，系统的大小，相互作用的强度和类型，以及系统的维数。此外，我们分析了费米子期望值的概率分布，当FSP严重时，它可以是非高斯的和厚尾的。作为一个实际应用，我们考虑电子和偶极原子在谐波约束，和均匀的电子气在温暖的稠密物质制度。此外，我们还提供了大量的PIMC数据，这些数据可以作为开发新方法的参考，也可以作为近似值的基准。
英文摘要：
The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC) simulations of fermions are severely restricted by the notorious fermion sign problem (FSP). In this work, we present a hands-on discussion of the FSP and investigate in detail its manifestation with respect to temperature, system size, interaction-strength and -type, and the dimensionality of the system. Moreover, we analyze the probability distribution of fermionic expectation values, which can be non-Gaussian and fat-tailed when the FSP is severe. As a practical application, we consider electrons and dipolar atoms in a harmonic confinement, and the uniform electron gas in the warm dense matter regime. In addition, we provide extensive PIMC data, which can be used as a reference for the development of new methods and as a benchmark for approximations.
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