路径积分蒙特卡罗模拟中的费米子符号问题：巨正则系综
Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble
摘要：
对巨正则系综下费米子路径积分蒙特卡罗模拟中的费米子符号问题进行了实际分析。作为一个代表性的模型系统，我们考虑电子在一个$2D$谐波陷阱。我们发现，在GCE的符号问题是更严重的比在正则系综在相同的条件下，这在一般情况下，使后者的首选选项。尽管存在这些困难，我们表明，在GCE中的费米PIMC模拟在许多情况下仍然是可行的，这可能会提供重要的数量，如可压缩性或松原格林函数。这对当代的研究领域有着重要的意义，比如热的致密物质、超冷原子和量子点中的电子。
英文摘要：
We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We find that the sign problem in the GCE is even more severe than in the canonical ensemble at the same conditions, which, in general, makes the latter the preferred option. Despite these difficulties, we show that fermionic PIMC simulations in the GCE are still feasible in many cases, which potentially gives access to important quantities like the compressiblity or the Matsubara Greens function. This has important implications for contemporary fields of research such as warm dense matter, ultracold atoms, and electrons in quantum dots.
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