arXiv subjects

Jan Vorberger

Publications and source records attributed to Jan Vorberger.

At least 55 records · Page 3Linked to original sources

arXiv2025

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on exact simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree -- quantities which are otherwise not directly accessible from the physical model -- from exact ab initio path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and non-equilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high density and high temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from exact quantum Monte Carlo simulations.

physics.chem-ph↗

arXiv2025

Fermionic free energies from \textit{ab initio} path integral Monte Carlo simulations of fictitious identical particles

We combine the recent $η-$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim \textit{et al.}, \textit{Phys.~Rev.~B} \textbf{111}, L041114 (2025)] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and fermionic limits [Xiong and Xiong, \textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)] to deal with the fermion sign problem. As a practical example, we apply our set-up to the warm dense uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange--correlation free energy down to half the Fermi temperature, and find excellent agreement with the state-of-the-art parametrization by Groth \textit{et al.}~[\textit{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)]. Our work opens up new avenues for the future study of a host of interacting Fermi-systems, including warm dense matter, ultracold atoms, and electrons in quantum dots.

cond-mat.quant-gas↗

arXiv2025

Strong geometry dependence of the X-ray Thomson Scattering Spectrum in single crystal silicon

We report on results from an experiment at the European XFEL where we measured the x-ray Thomson scattering (XRTS) spectrum of single crystal silicon with ultrahigh resolution. Compared to similar previous experiments, we consider a more complex scattering setup, in which the scattering vector changes orientation through the crystal lattice. In doing so, we are able to observe strong geometric dependencies in the inelastic scattering spectrum of silicon at low scattering angles. Furthermore, the high quality of the experimental data allows us to benchmark state-of-the-art TDDFT calculations, and demonstrate TDDFT's ability to accurately predict these geometric dependencies. Finally, we note that this experimental data was collected at a much faster rate than another recently reported dataset using the same setup, demonstrating that ultrahigh resolution XRTS data can be collected in more general experimental scenarios.

cond-mat.mtrl-sci↗

arXiv2024

Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulation results for the chemical potential of the warm dense uniform electron gas (UEG), spanning a broad range of densities and temperatures. This is achieved by following two independent routes, i) based on the direct estimation of the free energy [Dornheim \emph{et al.}, arXiv:2407.01044] and ii) using a histogram estimator in PIMC simulations with a varying number of particles. We empirically confirm the expected inverse linear dependence of the exchange--correlation (XC) part of the chemical potential on the simulated number of electrons, which allows for a reliable extrapolation to the thermodynamic limit without the necessity for an additional finite-size correction. We find very good agreement (within $Δμ_\textnormal{xc}\lesssim0.5\%$) with the previous parametrization of the XC-free energy by Groth \emph{et al.}~[\emph{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)], which constitutes an important cross validation of current state-of-the-art UEG equations of state. In addition to being interesting in its own right, our study constitutes the basis for the future PIMC based investigation of the chemical potential of real warm dense matter systems starting with hydrogen.

physics.chem-ph↗

arXiv2024

η-ensemble path integral Monte Carlo approach to the free energy of the warm dense electron gas and the uniform electron liquid

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.

physics.chem-ph↗

arXiv2024

Towards Model-free Temperature Diagnostics of Warm Dense Matter from Multiple Scattering Angles

Warm dense matter (WDM) plays an important role in astrophysical objects and technological applications, but the rigorous diagnostics of corresponding experiments is notoriously difficult. In this work, we present a model-free analysis of x-ray Thomson scattering (XRTS) measurements at multiple scattering angles. Specifically, we analyze scattering data that have been collected for isochorically heated graphite at the Linac Coherent Light Source (LCLS). Overall, we find good consistency in the extracted temperature between small and large scattering angles, whereas possible signatures of non-equilibrium may be hidden by the source function, and by the available dynamic spectral range. The present proof-of-principle study directly points to improved experimental set-ups for equation-of-state measurements and for the model-free study of relaxation times.

physics.plasm-ph↗

arXiv2024

On the density-density correlations of the non-interacting finite temperature electron gas

The density-density correlations of the non-interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic structure factor, thermal structure factor and imaginary time correlation function. Applications of these expressions in the classical mapping approach, self-consistent dielectric formalism and equation-of-state construction are analyzed in depth.

physics.plasm-ph↗

arXiv2024

Green's function perspective on the nonlinear density response of quantum many-body systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin-Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

cond-mat.str-el↗

arXiv2024

Nonlocal vs Local Pseudopotentials Affect Kinetic Energy Kernels in Orbital-Free DFT

The kinetic energy (KE) kernel, which is defined as the second order functional derivative of the KE functional with respect to density, is the key ingredient to the construction of KE models for orbital free density functional theory (OFDFT) applications. For solids, the KE kernel is usually approximated using the uniform electron gas (UEG) model or the UEG-with-gap model. These kernels do not have information about the effects from the core electrons since there are no orbitals for the projection on nonlocal pseudopotentials. To illuminate this aspect, we provide a methodology for computing the KE kernel from Kohn-Sham DFT and apply it to the valence electrons in bulk aluminum (Al) with a face-centered cubic lattice and in bulk silicon (Si) in a semiconducting crystal diamond state. We find that bulk-derived local pseudopotentials provide accurate results for the KE kernel in the interstitial region. The effect of using nonlocal pseudopotentials manifests at short wavelengths, defined by the diameter of an ion surrounded by its core electrons. Specifically, we find that the utilization of nonlocal pseudopotentials leads to significant deviations in the KE kernel from the von Weizsacker result in this region, which is, as a rule, explicitly enforced in most widely used KE functional approximations for OFDFT simulations.

cond-mat.mtrl-sci↗

arXiv2024

Effects of Mosaic Crystal Instrument Functions on X-ray Thomson Scattering Diagnostics

Mosaic crystals, with their high integrated reflectivities, are widely-employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 $μ$m and 100 $μ$m mosaic HAPG crystals, and how the broadening varies across the spectrometer in an energy range of 6.7-8.6 keV. Notably, we find a strong asymmetry in the shape of the IF towards higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas, and find that the temperature can be overestimated if an approximate symmetric IF is used. We therefore expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modelling and model-free approaches.

physics.plasm-ph↗

arXiv2024

Short wavelength limit of the dynamic Matsubara local field correction

We investigate the short wavelength limit of the dynamic Matsubara local field correction $\widetilde{G}(\mathbf{q},z_l)$ of the uniform electron gas based on direct \emph{ab initio} path integral Monte Carlo (PIMC) results over an unprecedented range of wavenumbers, $q\lesssim20q_\textnormal{F}$, where $q_\textnormal{F}$ is the Fermi wavenumber. We find excellent agreement with the analytically derived asymptotic limit by Hou \emph{et al.}~[\textit{Phys.~Rev.~B}~\textbf{106}, L081126 (2022)] for the static local field correction and empirically confirm the independence of the short wavelength limit with respect to the Matsubara frequency $z_l$. In the warm dense matter regime, we find that the onset of the quantum tail in the static local field correction closely coincides with the onset of the algebraic tail in the momentum distribution function and the corresponding empirical criterion reported by Hunger \emph{et al.}~[\textit{Phys.~Rev.~E} \textbf{103}, 053204 (2021)]. In the strongly coupled electron liquid regime, our calculations reveal a more complicated non-monotonic convergence towards the $q\to\infty$ limit that is shaped by the spatial structure in the system. We expect our results to be of broad interest for a number of fields including the study of matter under extreme conditions, the development of improved dielectric theories, and the construction of advanced exchange--correlation functionals for thermal density functional theory.

cond-mat.str-el↗

arXiv2024

Direct free energy calculation from ab initio path integral Monte Carlo simulations of warm dense matter

We carry out highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) simulations to directly estimate the free energy of various warm dense matter systems including the uniform electron gas and hydrogen without any nodal restrictions or other approximations. Since our approach is based on an effective ensemble in a bosonic configuration space, it does not increase the computational complexity beyond the usual fermion sign problem. Its application to inhomogeneous cases such as an electronic system in a fixed external ion potential is straightforward and opens up the enticing possibility to benchmark density functional theory and other existing methods. Finally, it is not limited to warm dense matter, and can be applied to a gamut of other systems such ultracold atoms and electrons in quantum dots.

cond-mat.quant-gas↗

arXiv2024

Quantum delocalization, structural order, and density response of the strongly coupled electron liquid

We investigate the impact of electronic correlations and quantum delocalization onto the static structure factor and static density response function of the strongly coupled electron liquid. In contrast to a classical system, the density response of the electron liquid vanishes on small length scales due to quantum delocalization effects, which we rigorously quantify in terms of imaginary-time correlation functions and dynamic Matsubara response functions. This allows us to analyze the interplay of structural order and dynamic quantum effects as it manifests in the dynamic Matsubara local field correction. Finally, we identify an effective electronic attraction in the spin-offdiagonal static density response when the wavelength of the perturbation is commensurate with the average interparticle distance.

physics.chem-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

Ultrahigh Resolution X-ray Thomson Scattering Measurements at the European XFEL

Using a novel ultrahigh resolution ($ΔE \sim 0.1\,$eV) 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.

physics.plasm-ph↗

arXiv2024

Dynamic exchange-correlation effects in the strongly coupled electron liquid

We present the first quasi-exact \textit{ab initio} path integral Monte Carlo (PIMC) results for the dynamic local field correction $\widetilde{G}(\mathbf{q},z_l;r_s,Θ)$ in the imaginary Matsubara frequency domain, focusing on the strongly coupled finite temperature uniform electron gas. These allow us to investigate the impact of dynamic exchange--correlation effects onto the static structure factor. Our results provide a straightforward explanation for previously reported spurious effects in the so-called \textit{static approximation} [Dornheim \textit{et al.}, \textit{Phys.~Rev.~Lett.}~\textbf{125}, 235001 (2020)], where the frequency-dependence of the local field correction is neglected. Our findings hint at the intriguing possibility of constructing an analytical four-parameter representation of $\widetilde{G}(\mathbf{q},z_l;r_s,Θ)$ valid for a substantial part of the phase diagram, which would constitute key input for thermal density functional theory simulations.

cond-mat.str-el↗

arXiv2024

Ultrafast Heating Induced Suppression of $d$-band Dominance in the Electronic Excitation Spectrum of Cuprum

The combination of isochoric heating of solids by free electron lasers (FEL) and in situ diagnostics by X-ray Thomson scattering (XRTS) allows for measurements of material properties at warm dense matter (WDM) conditions relevant for astrophysics, inertial confinement fusion, and material science. In the case of metals, the FEL beam pumps energy directly into electrons with the lattice structure of ions being nearly unaffected. This leads to a unique transient state that gives rise to a set of interesting physical effects, which can serve as a reliable testing platform for WDM theories. In this work, we present extensive linear-response time-dependent density functional theory (TDDFT) results for the electronic dynamic structure factor of isochorically heated copper with a face-centered cubic lattice. At ambient conditions, the plasmon is heavily damped due to the presence of $d$-band excitations, and its position is independent of the wavenumber. In contrast, the plasmon feature starts to dominate the excitation spectrum and has a Bohm-Gross type plasmon dispersion for temperatures $T \geq 4~{\rm eV}$, where the quasi-free electrons in the interstitial region are in the WDM regime. In addition, we analyze the thermal changes in the $d$-band excitations and outline the possibility to use future XRTS measurements of isochorically heated copper as a controlled testbed for WDM theories.

physics.chem-ph↗

arXiv2024

Excitation signatures of isochorically heated electrons in solids at finite wavenumber explored from first principles

Ultrafast heating of solids with modern X-ray free electron lasers (XFELs) leads to a unique set of conditions that is characterized by the simultaneous presence of heated electrons in a cold ionic lattice. In this work, we analyze the effect of electronic heating on the dynamic structure factor (DSF) in bulk Aluminium (Al) with a face-centered cubic lattice and in silicon (Si) with a crystal diamond structure using first-principles linear-response time-dependent density functional theory simulations. We find a thermally induced red shift of the collective plasmon excitation in both materials. In addition, we show that the heating of the electrons in Al can lead to the formation of a double-plasmon peak due to the extension of the Landau damping region to smaller wavenumbers. Finally, we demonstrate that thermal effects generate a measurable and distinct signature (peak-valley structure) in the DSF of Si at small frequencies. Our simulations indicate that there is a variety of new features in the spectrum of X-ray-driven solids, specifically at finite momentum transfer, which can probed in upcoming X-ray Thomson scattering (XRTS) experiments at various XFEL facilities.

physics.comp-ph↗