arXiv subjects

Maximilian Böhme

Publications and source records attributed to Maximilian Böhme.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic energy from the cubic sum rule of the dynamic structure factor

The third frequency moment sum rule of the dynamic structure factor $S(\mathbf{q},ω)$ is explored for the first time as an alternative estimator of the kinetic energy $K$ of quantum many-body systems. As a practical example, the uniform electron gas at warm dense matter conditions is considered. First, $K$ is extracted from quasi-exact \emph{ab initio} path integral Monte Carlo results for the imaginary-time density--density correlation function $F(\mathbf{q},τ)$ and the expected excellent self-consistency with the thermodynamic differentiation route is confirmed. Second, $K$ is extracted from approximate dielectric formalism results for $S(\mathbf{q},ω)$ and it is observed that common semi-classical approximations lead to a wave-number dependent $K$ with an incorrect short-wavelength limit. Our results are expected to be of broad interest for a great variety of applications, including time-dependent density functional theory, dielectric formalism schemes and warm dense matter models, as well as for the design of dedicated x-ray Thomson scattering experiments with the potential to provide model-free access to the full electronic equation of state.

physics.plasm-ph↗

arXiv2025

Static linear density response from X-ray Thomson scattering measurements: a case study of warm dense beryllium

Linear response theory is ubiquitous throughout physics and plays a central role in the theoretical description of warm dense matter -- an extreme state that occurs within compact astrophysical objects and that is traversed on the compression path of a fuel capsule in inertial confinement fusion applications. Here we show how one can relate the static linear density response function to X-ray Thomson scattering (XRTS) measurements, which opens up new possibilities for the diagnostics of extreme states of matter, and for the rigorous assessment and verification of theoretical models and approximations. As a practical example, we consider an XRTS data set of warm dense beryllium taken at the National Ignition Facility [T.~Döppner \emph{et al.}, \textit{Nature} \textbf{618}, 270-275 (2023)]. The comparison with state-of-the-art \emph{ab initio} path integral Monte Carlo (PIMC) simulations [T.~Dornheim \emph{et al.}, \textit{Nature Commun.}~(in print), arXiv:2402.19113] gives us a best estimate of the mass density of $ρ=18\pm6\,$g/cc, which is consistent with previous PIMC and density functional theory based studies, but rules out the original estimate of $ρ=34\pm4\,$g/cc based on a Chihara model fit.

physics.plasm-ph↗

arXiv2024

First principles simulations of dense hydrogen

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

physics.comp-ph↗

arXiv2024

Ab initio path integral Monte Carlo simulations of warm dense two-component systems without fixed nodes: structural properties

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)] $ξ$-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.

physics.comp-ph↗

arXiv2024

Unraveling electronic correlations in warm dense quantum plasmas

The study of matter at extreme densities and temperatures has emerged as a highly active frontier at the interface of plasma physics, material science and quantum chemistry with direct relevance for planetary modeling and inertial confinement fusion. A particular feature of such warm dense matter is the complex interplay of strong Coulomb interactions, quantum effects, and thermal excitations, rendering its rigorous theoretical description a formidable challenge. Here, we report a breakthrough in path integral Monte Carlo simulations that allows us to unravel this intricate interplay for light elements without nodal restrictions. This new capability gives us access to electronic correlations previously unattainable. As an example, we apply our method to strongly compressed beryllium to describe x-ray Thomson scattering (XRTS) data obtained at the National Ignition Facility. We find excellent agreement between simulation and experiment. Our analysis shows an unprecedented level of consistency for independent observations without the need for any empirical input parameters.

physics.plasm-ph↗

arXiv2023

Bound state breaking and the importance of thermal exchange-correlation effects in warm dense hydrogen

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.

physics.chem-ph↗

arXiv2023

Electronic density response of warm dense hydrogen on the nanoscale

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.

physics.plasm-ph↗

arXiv2023

Physical insights from imaginary-time density--density correlation functions

The accurate theoretical description of the dynamic properties of correlated quantum many-body systems such as the dynamic structure factor $S(\mathbf{q},ω)$ constitutes an important task in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary time density--density correlation function $F(\mathbf{q},τ)$ to real frequencies is a notoriously hard problem. In this work, we argue that no such analytic continuation is required as $F(\mathbf{q},τ)$ contains, by definition, the same physical information as $S(\mathbf{q},ω)$, only in an unfamiliar representation. Specifically, we show how we can directly extract key information such as the temperature or quasi-particle excitation energies from the $τ$-domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions. As a practical example, we consider \emph{ab initio} path integral Monte Carlo results for the uniform electron gas (UEG), and demonstrate that even nontrivial processes such as the \emph{roton feature} of the UEG at low density straightforwardly manifest in $F(\mathbf{q},τ)$. In fact, directly working in the $τ$-domain is advantageous for many reasons and holds the enticing promise for unprecedented agreement between theory and experiment.

cond-mat.stat-mech↗

arXiv2023

Extraction of the frequency moments of spectral densities from imaginary-time correlation function data

We introduce an exact framework to compute the positive frequency moments $M^{(α)}(\mathbf{q})=\braket{ω^α}$ of different dynamic properties from imaginary-time quantum Monte Carlo data. As a practical example, we obtain the first five moments of the dynamic structure factor $S(\mathbf{q},ω)$ of the uniform electron gas at the electronic Fermi temperature based on \emph{ab initio} path integral Monte Carlo simulations. We find excellent agreement with known sum rules for $α=1,3$, and, to our knowledge, present the first results for $α=2,4,5$. Our idea can be straightforwardly generalized to other dynamic properties such as the single-particle spectral function $A(\mathbf{q},ω)$, and will be useful for a number of applications, including the study of ultracold atoms, exotic warm dense matter, and condensed matter systems.

cond-mat.quant-gas↗

arXiv2022

Temperature analysis of X-ray Thomson scattering data

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

physics.plasm-ph↗

arXiv2022

Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [M.Böhme et. al. Phys.Rev.Lett.(in print)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair-potential. We find very favourable convergence behaviour towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyse in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations such as DFT. Our set-up gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange--correlation (XC) kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

physics.plasm-ph↗

arXiv2022

Ab initio Static Exchange-Correlation Kernel across Jacob's Ladder without functional derivatives

The electronic exchange-correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of material properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In practice, no reliable method has been known that allows to compute the kernel of real materials with arbitrary XC functionals. In this work, we overcome this long-standing limitation by introducing a new, formally exact methodology for the computation of the material specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives -- no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model at both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC-functionals, and has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that our framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.

physics.comp-ph↗

arXiv2022

Analyzing X-ray Thomson scattering experiments of warm dense matter in the imaginary-time domain: theoretical models and simulations

The rigorous diagnostics of experiments with warm dense matter (WDM) is notoriously difficult. A key method is given by X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [arXiv:2206.12805] have introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions (ITCF). On the one hand, switching from the frequency- to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without any models or approximations. On the other hand, the bulk of theoretical works in dynamic quantum many-body theory is devoted to the frequency-domain, and, to our knowledge, the manifestation of physics properties within the ITCF remains poorly understood. In the present work, we aim to change this unsatisfactory situation by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wave numbers, densities, and temperatures.

cond-mat.stat-mech↗

arXiv2022

Accurate Temperature Diagnostics for Matter under Extreme Conditions

The experimental investigation of matter under extreme densities and temperatures as they occur for example 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 highly difficult by the extreme conditions. In this work, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials from scattering experiments, without the need for any simulations or an explicit deconvolution. This new 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 gamut of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

physics.plasm-ph↗

arXiv2022

Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations

The properties of hydrogen under extreme conditions are important for many applications, including inertial confinement fusion and astrophysical models. A key quantity is given by the electronic density response to an external perturbation, which is probed in X-ray Thomson scattering (XRTS) experiments -- the state of the art diagnostics from which system parameters like the free electron density $n_e$, the electronic temperature $T_e$, and the charge state $Z$ can be inferred. In this work, we present highly accurate path integral Monte Carlo (PIMC) results for the electronic density response of hydrogen. We obtain the exchange-correlation (XC) kernel $K_{xc}$, which is of central relevance for many applications, such as time-dependent density functional theory (TD-DFT). This gives us a first unbiased look into the electronic density response of hydrogen in the warm-dense matter regime, thereby opening up a gamut of avenues for future research.

physics.comp-ph↗

arXiv2021

The Relevance of Electronic Perturbations in the Warm Dense Electron Gas

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental and theoretical physics and is challenging traditional concepts of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of X-Ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpoint where the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

physics.plasm-ph↗

arXiv2021

Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics

In a recent Letter, Dornheim et al. [PRL 125, 085001 (2020)] have investigated the nonlinear density response of the uniform electron gas in the warm dense matter regime. More specifically, they have studied the cubic response function at the first harmonic, which cannot be neglected in many situations of experimental relevance. In this work, we go one step further and study the full spectrum of excitations at the higher harmonics of the original perturbation based on extensive new ab initio path integral Monte Carlo (PIMC) simulations. We find that the dominant contribution to the density response beyond linear response theory is given by the quadratic response function at the second harmonic in the moderately nonlinear regime. Furthermore, we show that the nonlinear density response is highly sensitive to exchange-correlation effects, which makes it a potentially valuable new tool of diagnostics. To this end, we present a new theoretical description of the nonlinear electronic density response based on the recent effective static approximation to the local field correction [PRL 125, 235001 (2020)], which accurately reproduces our PIMC data with negligible computational cost.

physics.plasm-ph↗

arXiv2021

Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature without fixed nodes

We present extensive new \textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(\mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and temperatures. This allows us to study the nontrivial exchange--correlation induced increase of low-momentum states around the Fermi temperature, and to investigate its connection to the related lowering of the kinetic energy compared to the ideal Fermi gas. In addition, we investigate the impact of quantum statistics on both $n(\mathbf{k})$ and the off-diagonal density matrix in coordinate space, and find that it cannot be neglected even in the strongly coupled electron liquid regime. Our results were derived without any nodal constraints, and thus constitute a benchmark for other methods and approximations.

physics.comp-ph↗