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Using a novel ultrahigh resolution (\Delta E ~ 0.1eV) setup to measure electronic features in x-ray Thomson scattering (XRTS) experiments at the European XFEL in Germany, we have studied the collective plasmon excitation in aluminium at ambient conditions, which we can measure very accurately even at low momentum transfers. As a result, we can resolve previously reported discrepancies between ab initio time-dependent density functional theory simulations and experimental observations. The demonstrated capability for high-resolution XRTS measurements will be a game changer for the diagnosis of experiments with matter under extreme densities, temperatures, and pressures, and unlock the full potential of state-of-the-art x-ray free electron laser (XFEL) facilities to study planetary interior conditions, to understand inertial confinement fusion applications, and for material science and discovery.

We evaluate the f-sum rule on the dynamic structure factor in the imaginary-time domain as a formally exact and simulation-free means of normalizing X-Ray Thomson Scattering (XRTS) spectra. This circumvents error-prone real-time deconvolution of the source function and facilitates calculating the static structure factor from the properly normalized imaginary-time correlation function. We apply our technique to two distinct sets of experimental data, finding that it is effective for both narrow and broad x-ray sources. This approach could be readily adapted to other scattering spectroscopies.

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.

This repository contains all raw data pertaining to the figures in the publication "Dynamic exchange–correlation effects in the strongly coupled electron liquid", arXiv:2405.08480 Generally, files contain gnuplot formatted output using units shown in the figures. Exceptions are given by "Fig2.txt, Fig11_rs4.txt, Fig13_*.txt", where the relevant columns are given by: #1: q in a_B^{-1}; #2: integer Matsubara frequency index; #3: density response, not normalised by particle number

This repository contains all PIMC data associated with the publication "Quantum delocalization, structural order, and density response of the strongly coupled electron liquid". Files generally follow the same units as in the figures; in addition, raw data for Fig. 2 are structured as follows: Fig2b: #1 q [a_Bohr^{-1}]; #2 l; #3 Chi(q,z_l)x32 Fig2a: #1 q [a_Bohr^{-1}]; #2 tau [Ha^{-1}]; #3 F(q,tau)x32

This repository contains all PIMC results related to the publication "Ab initio Density Response and Local Field Factor of Warm Dense Hydrogen". Generally, data formats are identical to figures. Exceptions are 3D ITCF data sets for Figs. 2, 8 and 12: #1 k [a_Bohr^{-1}], #2 tau [Ha^{-1}], #3/#4 F(q,tau)x32 and statistical error and the "ITCF" folders with the raw data for F(q,tau): ITCF: #1 tau [Ha^{-1}]; #2/3: F(q,tau) and statistical error The number after "index" in the file names gives the number of the respective q-vector; see "static_structure_factor_key.dat", columns 1 and 2 for the respective index-to-q mapping, with [q]=a_Bohr{-1}

Hydrogen at extreme temperatures and pressures has significant relevance for cutting-edge technological applications, and its natural occurrence in astrophysical objects further underscores its importance. In this work, we develop a new framework to identify the breaking of bound states due to pressure ionization in bulk hydrogen [1]. Firstly, we show that the dimensionless reduced density gradient (RDG) is a valuable tool for detecting pressure-induced ionization in the medium. Secondly, the generalized RDG is proposed as an effective means for examining the interstitial electronic structure. Finally, our rigorous assessment of a variety of exchange-correlation (XC) functionals in density functional theory calculations for different density regions reveals the crucial role of thermal XC effects in accurately describing density gradients in high-energy density systems. Our exact path integral Monte-Carlo (PIMC) test set generated for this project is freely available online [2]. The insights gained from this research could also have implications for our understanding of astrophysical phenomena, such as white dwarf stars. Furthermore, this study is an addition to our current research on thermal effects in XC functionals, which we are exploring at various complexity levels [3-6]. References: [1] Z. Moldabekov, S. Schwalbe, M. P. Böhme, J. Vorberger, X. Shao, M. Pavanello, F. Graziani, T. Dornheim, Journal of Chemical Theory and Computation (in print) (2023). DOI: 10.1021/acs.jctc.3c00934 ; arXiv:2308.07916. [2] The data is available according to the FAIR principles on the bound state breaking BSB GitLab Repository. 2023; https://gitlab.com/theonov13/bsb [3] Z. Moldabekov, M. Lokamani, J. Vorberger, A. Cangi, and T. Dornheim, The Journal of Physical Chemistry Letters 14 (5), 1326-1333 (2023). [4] Z. Moldabekov, M. Lokamani, J. Vorberger, A. Cangi, T. Dornheim, J. Chem. Phys. 158, 094105 (2023). [5] Z. Moldabekov, T.Dornheim, M. Böhme, J. Vorberger, A. Cangi, J. Chem. Ph

Warm dense matter (WDM) is now routinely created and probed in laboratories around the world, providing unprecedented insights into conditions achieved in stellar atmospheres, planetary interiors, and inertial confinement fusion experiments. However, the interpretation of these experiments is often filtered through models with systematic errors that are difficult to quantify. Due to the simultaneous presence of quantum degeneracy and thermal excitation, processes in which free electrons are de-excited into thermally unoccupied bound states transferring momentum and energy to a scattered x-ray photon become viable [1]. Here we show that such free-bound transitions are a particular feature of WDM and vanish in the limits of cold and hot temperatures. The inclusion of these processes into the analysis of recent X-ray Thomson Scattering (XRTS) experiments on WDM at the National Ignition Facility [2] and the Linac Coherent Light Source [3] significantly improves model fits, indicating that free-bound transitions have been observed without previously being identified. This interpretation is corroborated by agreement with a recently developed model-free thermometry technique [4,5] and presents an important step for precisely characterizing and understanding the complex WDM state of matter. [1] M. Böhme et al, arXiv:2306.17653 [2] T. Döppner et al, Nature 618, 270-275 (2023) [3] D. Kraus et al, Plasma Phys. Control. Fusion 61, 014015 (2019) [4] T. Dornheim et al, Nature Communications 13, 7911 (2022) [5] T. Dornheim et al, Phys. Plasmas 30, 042707 (2023)

Experiments creating extreme states of matter almost invariably create non-equilibrium states. These are very interesting in their own right but need to be understood even if the ultimate goal is to probe high pressure or high temperature equilibrium properties like the equation of state. Here, we report on the capabilities of the newly developed imaginary time correlation function (ITCF) technique [1] to detect and quantify non-equilibrium in pump-probe experiments fielding time resolved x-ray scattering diagnostics. We find a high sensitivity of the ITCF even to a small fraction of non-equilibrium electrons in the Wigner distribution. The behavior of the ITCF technique is such that modern lasers and detectors should be able to trace the non-equilibrium relaxation from tens of femto-seconds to several 10s of picoseconds without the need for a model.

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, material science, and related disciplines. At finite temperatures, the gold standard is given by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, which do not require any empirical input, but exhibit an exponential increase in the required compute time for fermionic systems with increasing the system size N. Very recently, it has been suggested to compute fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles. In the present work, we use this technique to carry out very large (N≤1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of investigated properties, i.e., the static structure factor, the static density response function, and local field correction, over the entire range of length scales.

The properties of plasmas in the low-density limit are described by virial expansions. Analytical expressions are known from Green's function approaches only for the first three virial coefficients. Accurate path integral Monte Carlo (PIMC) simulations have recently been performed for the uniform electron gas, allowing the virial expansions to be analyzed and interpolation formulas to be derived. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of validity of the interpolation formula of Groth {\it et al.}~[Phys.~Rev.~Lett.~\textbf{119}, 135001 (2017)]. We discuss the fourth virial coefficient, which is of interest, e.g., for properties of solar plasmas, but has not yet been precisely known. Combining PIMC simulations with benchmarks from exact results of the virial expansion would allow us to obtain precise results for the equation of state (EoS) in a wide range of parameters.

We present new concepts for the experimental and theoretical study of atomic physics of Be at GBar pressure at the National Ignition Facility.

This repository contains the raw data for the relevant figures of the article "X-ray Thomson scattering absolute intensity from the f-sum rule in the imaginary-time domain". All data are standard gnuplot output.

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for a variety of structural properties of warm dense hydrogen and beryllium. To deal with the fermion sign problem -- an exponential computational bottleneck due to the antisymmetry of the electronic thermal density matrix -- we employ the recently proposed [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022); \textbf{159}, 164113 (2023)] -extrapolation method and find excellent agreement with exact direct PIMC reference data where available. This opens up the intriguing possibility to study a gamut of properties of light elements and potentially material mixtures over a substantial part of the warm dense matter regime, with direct relevance for astrophysics, material science, and inertial confinement fusion research.

Matter at extreme densities and temperatures displays a complex quantum behavior that is characterized by Coulomb interactions, thermal excitations, and partial ionization. Such warm dense matter (WDM) is ubiquitous throughout the universe and occurs in a host of astrophysical objects such as giant planet interiors and white dwarf atmospheres. A particularly intriguing application is given by inertial confinement fusion, where both the fuel capsule and the ablator have to traverse the WDM regime in a controlled way to reach ignition. In practice, rigorously understanding WDM is highly challenging both from experimental measurements and numerical simulations [1]. On the one hand, interpreting and diagnosing experiments with WDM requires a suitable theoretical description. One the other hand, there is no single method that is capable of accurately describing the full range of relevant densities and temperatures, and the interpretation of experiments is, therefore, usually based on a number of de-facto uncontrolled approximations. The result is the vicious cycle of WDM diagnostics: making sense of experimental observations requires theoretical modeling, whereas theoretical models must be benchmarked against experiments to verify their inherent assumptions. In this work, we outline a strategy to break this vicious cycle by combining the X-ray Thomson scattering (XRTS) technique [2] with new ab initio path integral Monte Carlo (PIMC) capabilities [3,4,5]. As a first step, we have proposed to interpret XRTS experiments in the imaginary-time (Laplace) domain, which allows for the model-free diagnostics of the temperature [6] and normalization [7]. Moreover, by switching to the imaginary-time, we can directly compare our quasi-exact PIMC calculations with the experimental measurement [5]. This opens up novel ways to diagnose the experimental conditions, as we have recently demonstrated for the case of strongly compressed beryllium at the National Ignition Facility. Our resu

Matter at extreme densities and temperatures displays a complex quantum behavior that is characterized by Coulomb interactions, thermal excitations, and partial ionization. Such warm dense matter (WDM) is ubiquitous throughout the universe and occurs in a host of astrophysical objects such as giant planet interiors and white dwarf atmospheres. A particularly intriguing application is given by inertial confinement fusion, where both the fuel capsule and the ablator have to traverse the WDM regime in a controlled way to reach ignition. In practice, rigorously understanding WDM is highly challenging both from experimental measurements and numerical simulations [1]. On the one hand, interpreting and diagnosing experiments with WDM requires a suitable theoretical description. One the other hand, there is no single method that is capable of accurately describing the full range of relevant densities and temperatures, and the interpretation of experiments is, therefore, usually based on a number of de-facto uncontrolled approximations. The result is the vicious cycle of WDM diagnostics: making sense of experimental observations requires theoretical modeling, whereas theoretical models must be benchmarked against experiments to verify their inherent assumptions. In this work, we outline a strategy to break this vicious cycle by combining the X-ray Thomson scattering (XRTS) technique [2] with new ab initio path integral Monte Carlo (PIMC) capabilities [3,4,5]. As a first step, we have proposed to interpret XRTS experiments in the imaginary-time (Laplace) domain, which allows for the model-free diagnostics of the temperature [6] and normalization [7]. Moreover, by switching to the imaginary-time, we can directly compare our quasi-exact PIMC calculations with the experimental measurement [5]. This opens up novel ways to diagnose the experimental conditions, as we have recently demonstrated for the case of strongly compressed beryllium at the National Ignition Facility. Our resu

The finite temperature version of the Vashishta–Singwi (VS) dielectric scheme for the paramagnetic warm dense uniform electron fluid is revisited correcting for an earlier thermodynamic derivative error. The VS scheme handles quantum mechanical effects at the level of the random phase approximation and treats correlations via the density expansion of a generalized Singwi-Tosi-Land-Sjölander (STLS) closure that inserts a parameter determined by enforcing the compressibility sum rule. Systematic comparison with quasi-exact results, based on quantum Monte Carlo simulations, reveals a structural superiority of the VS scheme towards strong coupling and a thermodynamic superiority of the STLS scheme courtesy of a favorable cancellation of errors. Guidelines are provided for the construction of dielectric schemes that are expected to be more accurate but computationally costly.

This repository contains the raw data for the publication "Ab initio path integral Monte Carlo simulations of warm dense two-component systems without fixed nodes: structural properties". All units as described in the paper / figure captions.

A Fourier–Matsubara series expansion is derived for imaginary–time correlation functions that constitutes the imaginary–time generalization of the infinite Matsubara series for equal-time correlation functions. The expansion is consistent with all known exact properties of imaginary–time correlation functions and opens up new avenues for the utilization of quantum Monte Carlo simulation data. Moreover, the expansion drastically simplifies the computation of imaginary–time density–density correlation functions with the finite temperature version of the self-consistent dielectric formalism. Its existence underscores the utility of imaginary–time as a complementary domain for many-body physics.

We present a new methodology for the linear-response time-dependent density functional theory (LR-TDDFT) calculation of the dynamic density response function of warm dense matter in an adiabatic approximation that can be used with any available exchange-correlation (XC) functional across Jacob's Ladder and across temperature regimes. The main novelty of the presented approach is that it can go beyond the adiabatic local density approximation (ALDA) and generalized LDA (AGGA) while preserving the self-consistence between the Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems. The key ingredient for the presented method is the combination of the adiabatic XC kernel from the direct perturbation approach with the macroscopic dynamic KS response from the standard LR-TDDFT method using KS orbitals. We demonstrate the application of the method for the example of warm dense hydrogen, for which we perform a detailed analysis of the KS density response function, the RPA result, the total density response function and of the adiabatic XC kernel. The analysis is performed using LDA, GGA, and meta-GGA level approximations for the XC effects. The presented method is directly applicable to disordered systems such as liquid metals, warm dense matter, and dense plasmas.

Warm dense matter (WDM)---an extreme state that is characterized by extreme densities and temperatures---has emerged as one of the most active frontiers in plasma physics and material science. In nature, WDM occurs in astrophysical objects such as giant planet interiors and brown dwarfs. In addition, WDM is highly important for cutting-edge technological applications such as inertial confinement fusion and the discovery of novel materials. In the laboratory, WDM is studied experimentally in large facilities around the globe, and new techniques have facilitated unprecedented insights. Yet, the interpretation of these experiments requires a reliable diagnostics based on accurate theoretical modeling, which is a notoriously difficult task [1]. In this work, I will give an overview of how we can use exact ab-initio path integral Monte Carlo (PIMC) simulations [2] to get new insights into the behavior of WDM. Moreover, I will show how switching to the imaginary- time representation allows us to significantly improve the interpretation of X-ray Thomson scattering (XRTS) experiments, which are a key diagnostic for WDM [3]. Specifically, I will present a model-free temperature diagnostic [4] based on the well-known principle of detailed balance, but available for all wave numbers, and a new idea to directly extract the electron— electron static structure factor from an XRTS measurement [5]. As an outlook, I will show how new PIMC capabilities will allow to give us novel insights into electronic correlations in warm dense quantum plasmas, leading to unprecedented agreement between experiments [6] and theory. [1] M. Bonitz et al., Physics of Plasmas 27, 042710 (2020) [2] M. Böhme et al., Physical Review Letters 129, 066402 (2022) [3] S. Glenzer and R. Redmer, Reviews of Modern Physics 81, 1625 (2009) [4] T. Dornheim et al., Nature Communications 13, 7911 (2022) [5] T. Dornheim et al., arXiv:2305.15305 (submitted) [6] T. Döppner et al., Nature 618, 270-275 (2023)

The experimental investigation of matter under extreme densities and temperatures, as in astrophysical objects and nuclear fusion applications, constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered difficult at these extreme conditions. Here, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials in thermal equilibrium from X-ray Thomson scattering experiments, without the need for any simulations or an explicit deconvolution. Our paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a variety of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

Matter under extreme densities and temperatures is ubiquitous throughout our universe and naturally occurs in a plethora of astrophysical objects such as giant planet interiors and brown dwarfs. In addition, such warm dense matter (WDM) is of key importance for a number of technological applications, most notably inertial confinement fusion. Yet, the accurate diagnostics of experiments with WDM is rendered challenging by the extreme conditions. Indeed, even basic parameters such as the temperature often cannot be measured directly and have to be inferred from other observations. In this context, X-ray Thomson scattering (XRTS) [1] has emerged as a key diagnostic, but the interpretation of an XRTS signal is often based on de-facto uncontrolled approximations such as the decomposition into bound and free electrons within the popular Chihara model. In this contribution, I outline how one can get direct access to the physical properties of interest by analyzing the measured signal in the imaginary-time domain [2]. No simulations/models and, therefore, no approximations are required. First and foremost, this allows us to infer the temperature of a given system with high accuracy [3]. Moreover, we can use XRTS to probe electron—electron correlations by utilizing the f-sum rule in the imaginary-time domain [4]. Finally, we show how the idea of imaginary-time correlation functions can be generalized to characterize the degree of nonequilibrium in the probed system [5], with important implications for equation-of-state measurements and the understanding of relaxation times. [1] S. Glenzer and R. Redmer, Reviews of Modern Physics 81, 1625 (2009) [2] T. Dornheim et al, arXiv:2209.02254 (submitted) [3] T. Dornheim et al, Nature Communications 13, 7911 (2022) [4] T. Dornheim et al, arXiv:2305.15305 (submitted) [5] J. Vorberger et al, arXiv:2302.11309 (submitted)

We have developed an experimental platform for x-ray Thomson scattering (XRTS) at NIF to characterize plasma conditions in ICF indirectly-driven capsule implosions near stagnation [1,2]. This enabled us to investigate up to 30 times compressed ablator materials reaching pressures above 3 Gigabars, at conditions where the distance between the nuclei becomes comparable to the extent of the core shell bound states, which will eventually lead to their pressure ionization. In this talk we will present results from experiments with beryllium shells. We observe reduced elastic scattering for the most extreme conditions [2]. We interpret this reduction as the precursor of pressure ionization of the remaining K-shell electrons, that is, a strongly modified bound state. The beryllium charge state inferred from the data is considerable higher than standard models predict but agrees well with results from DFT simulations [2,3]. Accurate modelling of the K-shell occupation of light elements is imperative for creating predictive capabilities for ICF implosions. Our experiments yield valuable benchmarks for this process and demonstrating a complex pathway of pressure ionization.

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ionic configurations, obtained by DFT-MD simulations, in order to solve the electronic problem for hydrogen under warm dense matter conditions. To solve the divergence problem in the Ewald-sum for attractive potentials we employ the pair-approximation. This approach is compared against the much simpler Kelbg pair-potential. We find very favorable convergence behavior towards the latter. Since PIMC does not require any further assumptions regarding exchange and correlations of the many-body system, we then compare electronic densities obtained from our snapshot PIMC calculations with DFT calculations in the metallic regime. Furthermore, we investigate the manifestation of the resulting fermionic sign problem in our snapshot PIMC simulations. This gives us the unique capability to study the properties of warm dense hydrogen from ab initio simulations without any further assumptions, like the functional form of the exchange-correlation effects or fixed fermionic nodes. Thus, snapshot PIMC enables us to obtain the exact density response of warm dense hydrogen. This is extremely valuable to both experiments, like X-Ray Thomson scattering, as well as the development of new XC-functionals.

Warm dense matter (WDM) is now routinely created and probed in laboratories around the world, providing unprecedented insights into conditions achieved in stellar atmospheres, planetary interiors, and inertial confinement fusion experiments. However, the interpretation of these experiments is often filtered through models with systematic errors that are difficult to quantify. Due to the simultaneous presence of quantum degeneracy and thermal excitation, processes in which free electrons are de-excited into thermally unoccupied bound states transferring momentum and energy to a scattered x-ray photon become viable [1]. Here we show that such free-bound transitions are a particular feature of WDM and vanish in the limits of cold and hot temperatures. The inclusion of these processes into the analysis of recent X-ray Thomson Scattering experiments on WDM at the National Ignition Facility [2] and the Linac Coherent Light Source [3] significantly improves model fits, indicating that free-bound transitions have been observed without previously being identified. This interpretation is corroborated by agreement with a recently developed model-free thermometry technique [4,5] and presents an important step for precisely characterizing and understanding the complex WDM state of matter. [1] M. Böhme et al, arXiv:2306.17653 [2] T. Döppner et al, Nature 618, 270-275 (2023) [3] D. Kraus et al, PPCF 61, 014015 (2019) [4] T. Dornheim et al, Nature Commun 13, 7911 (2022) [5] T. Dornheim et al, POP 30, 042707 (2023)

The experimental investigation of matter under extreme densities and temperatures, as in astrophysical objects and nuclear fusion applications, constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered difficult at these extreme conditions. Here, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials in thermal equilibrium from X-ray Thomson scattering experiments, without the need for any simulations or an explicit deconvolution [1,2]. Our paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a variety of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

Orbital-free density functional theory constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends on the employed kinetic energy (KE) density functional, which has to be supplied as an external input. In this work we consider several nonlocal and Laplacian-level KE functionals and use an external harmonic perturbation to compute the static density response at T=0 K in the linear and beyond-linear response regimes. We test for the satisfaction of exact conditions in the limit of uniform densities and for how approximate KE functionals reproduce the density response of realistic materials (e.g., Al and Si) against the Kohn-Sham DFT reference, which employs the exact KE. The results illustrate that several functionals violate exact conditions in the uniform electron gas (UEG) limit. We find a strong correlation between the accuracy of the KE functionals in the UEG limit and in the strongly inhomogeneous case. This empirically demonstrates the importance of imposing the limit of UEG response for uniform densities and validates the use of the Lindhard function in the formulation of kernels for nonlocal functionals. This conclusion is substantiated by additional calculations for bulk aluminum (Al) with a face-centered cubic (fcc) lattice and silicon (Si) with an fcc lattice, body-centered cubic (bcc) lattice, and semiconducting crystal diamond state. The analysis of fcc Al, and fcc as well as bcc Si data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that are subject to density inhomogeneities induced by ions.

Hydrogen at extreme temperatures and pressures is ubiquitous throughout our universe and naturally occurs in a variety of astrophysical objects. In addition, it is of key relevance for cutting-edge technological applications, with inertial confinement fusion research being a prime example. In the present work, we present exact \emph{ab initio} path integral Monte Carlo (PIMC) results for the electronic density of warm dense hydrogen along a line of constant degeneracy across a broad range of densities. Using the well-known concept of reduced density gradients, we develop a new framework to identify the breaking of bound states due to pressure ionization in bulk hydrogen. Moreover, we use our PIMC results as a reference to rigorously assess the accuracy of a variety of exchange--correlation (XC) functionals in density functional theory calculations for different density regions. Here a key finding is the importance of thermal XC effects for the accurate description of density gradients in high-energy density systems. Our exact PIMC test set is freely available online and can be used to guide the development of new methodologies for the simulation of warm dense matter and beyond.

All data as needed to generate the figures in the manuscript.

The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us new insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory.

A novel dielectric scheme is proposed for strongly coupled electron liquids that handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of classical liquids. The self-consistent scheme features a complicated dynamic local field correction functional and its formulation is guided by ab initio path integral Monte Carlo simulations. Remarkably, our scheme is capable to provide unprecedently accurate results for the static structure factor with the exception of the Wigner crystallization vicinity, despite the absence of adjustable or empirical parameters.

Matter at extreme temperatures and pressures -- commonly known as warm dense matter (WDM) in the literature -- is ubiquitous throughout our Universe and occurs in a number of astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion, and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are routinely probed in x-ray Thomson scattering (XRTS) experiments, and, in addition, are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear-response theory as well as nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques including ab initio path integral Monte Carlo (PIMC) simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrarily complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.