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Tobias Dornheim

Publications and source records attributed to Tobias Dornheim.

At least 91 records · Page 5Linked to original sources
arXiv2023

Virial coefficients of the Uniform Electron Gas from Path Integral Monte Carlo Simulations

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.

physics.plasm-ph↗
arXiv2023

Imposing Correct Jellium Response Is Key to Predict the Density Response by Orbital-Free DFT

Orbital-free density functional theory (OF-DFT) 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 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 (cd) 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.

physics.comp-ph↗
arXiv2023

Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles

The \emph{ab initio} path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion sign problem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the sign problem by carrying out PIMC simulations of fictitious systems which contain an interpolating continuous variable $ξ\in[-1,1]$ in their partition function, with the physical Fermi- and Bose-statistics corresponding to the endpoint limits $ξ=-1$ and $ξ=1$. It has been proposed that thermodynamic information about the fermionic limit might be obtained by path integral calculations within the bosonic sector $ξ>0$ combined with a quadratic $ξ$ extrapolation throughout the fermionic sector $ξ<0$, essentially bypassing the sign problem. In this work, we show how the inclusion of the artificial parameter $ξ$ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We empirically demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the archetypal uniform electron gas (UEG), where we find excellent agreement ($\sim0.5\%$) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding eleven orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

physics.comp-ph↗
arXiv2023

Evidence of free-bound transitions in warm dense matter and their impact on equation-of-state measurements

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. 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 and the Linac Coherent Light Source 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 and presents an important step for precisely characterizing and understanding the complex WDM state of matter.

physics.plasm-ph↗
arXiv2023

Averaging over atom snapshots in linear-response TDDFT of disordered systems: A case study of warm dense hydrogen

Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot--dependence of the electronic density response function and related properties. We present a consistent scheme for the computation of the macroscopic Kohn-Sham (KS) density response function connecting an average over snapshot values of charge density perturbations to the averaged values of KS potential variations. This allows us to formulate the LR-TDDFT within the adiabatic (static) approximation for the exchange-correlation (XC) kernel for disordered systems, where the static XC kernel is computed using the direct perturbation method [Moldabekov et al., J. Chem. Theory Comput. 19, 1286 (2023)]. The presented approach allows one to compute the macroscopic dynamic density response function as well as the dielectric function with a static XC kernel generated for any available XC functional. The application of the developed workflow is demonstrated for the example of warm dense hydrogen. The presented approach is applicable for various types of extended disordered systems such as warm dense matter, liquid metals, and dense plasmas.

physics.comp-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

Unravelling the nonlinear ideal density response of many-body systems

Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic, quartic and quintic responses reveal a deep connection with the linear response. Careful analysis of the static long wavelength limit led us to conjecture a canonical non-interacting form that expresses arbitrary order nonlinear responses as the weighted sum of the linear responses evaluated at all multiple harmonics. This harmonic expansion is successfully validated against ab initio path integral Monte Carlo simulations

cond-mat.quant-gas↗
arXiv2023

Prediction of a roton-type feature in warm dense hydrogen

In a recent Letter [T. Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{121}, 255001 (2018)], it was predicted on the basis of \textit{ab initio} quantum Monte Carlo simulations that, in a uniform electron gas, the peak $ω_0$ of the dynamic structure factor $S(q,ω)$ exhibits an unusual non-monotonic wave number dependence, where $dω_0/dq < 0$, at intermediate $q$, under strong coupling conditions. This effect was subsequently explained by the pair alignment of electrons %at an intermediate range of wave numbers [T. Dornheim \textit{et al.}, Comm. Phys. \textbf{5}, 304 (2022)]. Here we predict that this non-monotonic dispersion resembling the roton-type behavior known from superfluids should be observable in a dense, partially ionized hydrogen plasma. Based on a combination of path integral Monte Carlo simulations and linear response results for the density response function, we present the approximate range of densities, temperatures and wave numbers and make predictions for possible experimental observations.

physics.plasm-ph↗
arXiv2023

Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids

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.

cond-mat.stat-mech↗
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

Revealing Non-equilibrium and Relaxation in Warm Dense Matter

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.

physics.plasm-ph↗
arXiv2023

Energy response and spatial alignment of the perturbed electron gas

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the harmonically perturbed uniform electron gas (UEG) for different densities and temperatures. This allows us to study the linear response of the UEG with respect to different contributions to the total energy for different wave numbers. We find that the induced change in the interaction energy exhibits a non-monotonic behaviour, and becomes negative for intermediate wave numbers. This effect is strongly dependent on the coupling strength and can be traced back to the spatial alignment of electrons introduced in earlier works [T.~Dornheim \emph{et al.}, Communications Physics \textbf{5}, 304 (2022)]. The observed quadratic dependence on the perturbation amplitude in the limit of weak perturbations and the quartic dependence of the perturbation amplitude corrections are consistent with linear and non-linear versions of the density stifness theorem. All PIMC simulation results are freely available online and can be used to benchmark new methods, or as input for other calculations.

cond-mat.quant-gas↗
arXiv2023

Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange--correlation kernels

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.

physics.comp-ph↗
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

Electronic Density Response of Warm Dense Matter

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.

physics.plasm-ph↗
arXiv2022

Non-empirical mixing coefficient for hybrid XC functionals from analysis of the XC kernel

We present an analysis of the static exchange-correlation (XC) kernel computed from hybrid functionals with a single mixing coefficient such as PBE0 and PBE0-1/3. We break down the hybrid XC kernels into the exchange and correlation parts using the Hartree-Fock functional, the exchange-only PBE, and the correlation-only PBE. This decomposition is combined with exact data for the static XC kernel of the uniform electron gas and an Airy gas model within a subsystem functional approach. This gives us a tool for the nonempirical choice of the mixing coefficient at ambient and extreme conditions. Our analysis provides physical insights into the effect of the variation of the mixing coefficient in hybrid functionals, which is of immense practical value. The presented approach is general and can be used for other type of functionals like screened hybrids.

physics.chem-ph↗