η-系综路径积分蒙特卡罗方法计算暖密电子气与均匀电子液体的自由能
η-ensemble path integral Monte Carlo approach to the free energy of the warm dense electron gas and the uniform electron liquid
AI总结：
本文探索η-系综路径积分蒙特卡罗方法直接计算均匀电子气在暖密物质和强耦合区域的自由能，验证了算法细节并首次给出低密度区域的PIMC自由能结果。
摘要：
我们探索了最近引入的η-系综方法，该方法直接从第一性原理路径积分蒙特卡罗（PIMC）模拟中计算自由能 [T.~Dornheim 等人, arXiv:2407.01044]，并将其应用于典型的均匀电子气模型，涵盖暖密物质和强耦合区域。具体而言，我们对相关算法细节进行了深入研究，例如自由权重参数的选择，以及连接真实非理想系统（η=1）与理想极限（η=0）的最佳中间η步数的选择。此外，我们探索了总自由能对不同参数区域的固有分解，将其分解为理想玻色子贡献、理想到相互作用贡献以及玻色子到费米子贡献。最后，我们将新的自由能数据与通过绝热连接公式评估获得的现有自由能参数化结果 [Groth 等人, Phys.~Rev.~Lett.~\textbf{119}, 135001 (2017)] 进行了比较，发现在其适用范围内（即密度参数 r_s≤20）两者非常吻合；此外，我们首次给出了低密度区域 20 < r_s≤100 下自由能的 PIMC 结果。我们期望这些结果不仅对极端条件下物质的研究有意义，也对更广泛的相互作用量子多体系统 PIMC 模拟领域具有重要意义。
英文摘要：
We explore the recently introduced $η$-ensemble approach to compute the free energy directly from \emph{ab initio} path integral Monte Carlo (PIMC) simulations [T.~Dornheim \emph{et al.}, arXiv:2407.01044] and apply it to the archetypal uniform electron gas model both in the warm dense matter and strongly coupled regimes. Specifically, we present an in-depth study of the relevant algorithmic details such as the choice of the free weighting parameter and the choice of the optimum number of intermediate $η$-steps to connect the real, non-ideal system ($η=1$) with the ideal limit ($η=0$). Moreover, we explore the inherent decomposition of the full free energy into its ideal bosonic, ideal-to-interacting, and bosonic-to-fermionic contributions for different parameter regimes. Finally, we compare our new free energy data with an existing free energy parametrization [Groth \emph{et al.}, Phys.~Rev.~Lett.~\textbf{119}, 135001 (2017)] obtained via adiabatic connection formula evaluations, and we find very good agreement in its range of applicability, i.e., for density parameters $r_s\leq20$; in addition, we present the first PIMC results for the free energy in the low density regime of $20 < r_s\leq 100$. We expect our results to be of interest both for the study of matter under extreme conditions, as well as to the more general field of PIMC simulations of interacting quantum many-body systems.
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