Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

Abstract

In a recent letter [Phys. Rev. Lett. 125, 085001 (2020)], Dornheim et al. have presented the first ab initio path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/fourbody correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange–correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities (rs = 0.5, . . . , 10) and temperatures (θ = 0.01, . . . , 4). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe threeand potentially even four-body correlation functions in WDM. Introduction. – Warm dense matter (WDM) [1], an extreme state with high temperatures T ∼ 10 − 10k and densities comparable or even exceeding the density of solids, constitutes one of the most active frontiers in plasma physics, material science, and related disciplines. In nature, these conditions occur in astrophysical objects such as giant planet interiors [2, 3], the core of brown dwarfs [4, 5], and neutron star crusts [6]. In addition, WDM is highly relevant for cutting-edge technological applications like hot-electron chemistry [7], the discovery of novel materials [8,9], and inertial confinement fusion [10]– the latter offering a potential abundance of clean energy upon being fully mastered. For these reasons, WDM is created experimentally in large research facilities around the globe, such as NIF and LCLS in the United States, or the brand-new European X-FEL in Germany. A topical review of experimental techniques has been presented by Falk [11]. At the same time, the accurate theoretical description of WDM is most challenging [12–14] due to the intricate and nontrivial interplay of a) Coulomb correlations (often ruling out perturbation expansions like Green functions [15, 16]), b) quantum degeneracy effects like Pauli blocking (which prevents semi-classical methods like standard molecular dynamics), and c) thermal excitations (sparking the need of a full thermodynamic description beyond the ground state). These conditions are typically specified by two characteristic parameters that are both of the order of unity [17]: the density parameter, also known as the Wigner-Seitz radius, rs = r/aB (with r and aB being the average inter-particle distance and Bohr radius) and the degeneracy temperature θ = kBT/EF (with EF = q 2 F/2 being the usual Fermi energy [18], and qF the corresponding wave number). While no single method that is capable to accurately describe all aspects of WDM currently exists, density functional theory (DFT) has emerged as the de-facto work horse of WDM theory as it combines a manageable computational effort with an often tolerable level of systematic error [19]. At the same time, the accuracy of DFT crucially depends on the employed exchange–correlation (XC) functional [20, 21], which is an external input and, thus, cannot be obtained within DFT itself. Furthermore, the performance of different XC-functionals at WDM conditions is much less understood compared to the electronic ground state, which makes both the benchmarking of existing functionals [22,23] and the development of new ones [24–26] extremely important. A second limitation of contemporary WDM theory is that it is often based on linear response theory (LRT), i.e., the assumption of a linear answer of the electrons to an external perturbation [27]. This is certainly understandable, as a thorough theoretical description of nonlinear effects is substantially more complicated than LRT [28–34]. p-1 ar X iv :2 10 6. 04 89 9v 1 [ ph ys ic s. pl as m -p h] 9 J un 2 02 1