Energy functionals serve as the basis for different models and methods in quantum and classical many-particle physics. Arguably, one of the most successful and widely used approaches in material science at both ambient and extreme conditions is density functional theory (DFT). Various flavors of DFT methods are being actively used to study material properties at extreme conditions, such as in warm dense matter, dense plasmas, and nuclear physics applications. In this review, we focus on the warm dense matter regime, which occurs in the core of giant planets and stellar atmospheres, and as a transient state in inertial confinement fusion experiments. We discuss the connection between linear density response functions and free energy functionals as well as the utility of the linear response formalism for the construction of advanced functionals. As a new result, we derive the stiffness theorem linking the change in the intrinsic free energy to the density response properties of electrons. We review and summarize recent works that assess various exchange–correlation (XC) functionals for an inhomogeneous electron gas that is perturbed by a harmonic external field and for warm dense hydrogen using exact path integral quantum Monte Carlo data as an unassailable benchmark. This constitutes a valuable guide for selecting an appropriate XC functional for DFT calculations in the context of investigating the inhomogeneous electronic structure of warm dense matter. We stress that correctly simulating the strongly perturbed electron gas necessitates the correct UEG limit of the XC and non-interacting free-energy functionals.

中文翻译：

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从密度响应到能量泛函再返回：极端条件下物质的从头到尾视角


能量泛函是量子和经典多粒子物理学中不同模型和方法的基础。可以说，密度泛函理论 （DFT） 是环境条件和极端条件下材料科学中最成功和应用最广泛的方法之一。各种 DFT 方法正被积极用于研究极端条件下的材料特性，例如在温暖的致密物质、致密等离子体和核物理应用中。在这篇综述中，我们重点介绍了发生在巨行星和恒星大气层核心的暖致密物质状态，以及惯性约束聚变实验中的瞬态状态。我们讨论了线性密度响应函数和自由能泛函之间的联系，以及线性响应形式在构建高级泛函中的效用。作为一个新的结果，我们推导出了刚度定理，将本征自由能的变化与电子的密度响应特性联系起来。我们回顾和总结了最近的工作，这些工作使用精确路径积分量子蒙特卡洛数据作为无懈可击的基准，评估了受谐波外场扰动的非均匀电子气体和温暖致密氢的各种交换相关 （XC） 泛函。这构成了在研究暖致密物质的非均匀电子结构的情况下为 DFT 计算选择合适的 XC 函数的宝贵指南。我们强调，正确模拟强扰动的电子气体需要正确的 XC 和非相互作用自由能泛函的 UEG 极限。