Yilmaz A, Hunger K, Dornheim T, Groth S, Bonitz M
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany.
Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.
J Chem Phys. 2020 Sep 28;153(12):124114. doi: 10.1063/5.0022800.
Quantum Monte Carlo (QMC) belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof et al. [Contrib. Plasma Phys. 51, 687 (2011)] that allowed for the first ab initio simulations for dense quantum plasmas [Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. CPIMC also has a sign problem that occurs when the density is lowered, i.e., in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter-the ratio of the interparticle distance to the Bohr radius-r=r¯/a≲1. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two different versions of "restricted CPIMC"-called RCPIMC and RCPIMC+-where certain sign changing Monte Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has no sign problem at all, but it introduces a systematic error and is less accurate than RCPIMC+, which neglects only a smaller class of the Monte Carlo steps. Here, we report extensive simulations for the ferromagnetic uniform electron gas with which we investigate the properties and accuracy of RCPIMC and RCPIMC+. Furthermore, we establish the parameter range in the density-temperature plane where these simulations are both feasible and accurate. The conclusion is that RCPIMC and RCPIMC+ work best at temperatures in the range of Θ = kT/E ∼ 0.1…0.5, where E is the Fermi energy, allowing to reach density parameters up to r ∼ 3…5, thereby partially filling a gap left open by existing ab initio QMC methods.
量子蒙特卡罗（QMC）属于量子多粒子系统中最精确的模拟技术。然而，对于费米子，这些模拟受到符号问题的阻碍，该问题禁止在强简并区域进行模拟。随着Schoof等人开发的配置路径积分蒙特卡罗（CPIMC）[《等离子体物理贡献》51, 687 (2011)]，情况发生了变化，它首次实现了对致密量子等离子体的从头算模拟[Schoof等人，《物理评论快报》115, 130402 (2015)]。CPIMC也存在一个符号问题，当密度降低时会出现，即在与坐标空间中传统QMC互补的参数范围内。因此，对于温暖致密电子气的CPIMC模拟仅限于布鲁克纳参数的小值——粒子间距离与玻尔半径的比值——r = r¯/a≲1。为了用CPIMC达到更强耦合（更低密度）的区域，我们在此研究对蒙特卡罗程序的额外限制。特别是，我们引入了两种不同版本的“受限CPIMC”——称为RCPIMC和RCPIMC +——其中某些改变符号的蒙特卡罗更新被省略。有趣的是，其中一种方法（RCPIMC）根本没有符号问题，但它会引入系统误差，并且不如RCPIMC +精确，RCPIMC +只忽略了一小类蒙特卡罗步骤。在此，我们报告了对铁磁均匀电子气的广泛模拟，通过这些模拟我们研究了RCPIMC和RCPIMC +的性质和精度。此外，我们确定了在密度 - 温度平面中这些模拟既可行又精确的参数范围。结论是，RCPIMC和RCPIMC +在温度范围Θ = kT/E ∼ 0.1…0.5时效果最佳, 其中E是费米能量，这使得能够达到高达r ∼ 3…5的密度参数，从而部分填补了现有从头算QMC方法留下的空白。
