arXiv subjects

Tobias Dornheim

Publications and source records attributed to Tobias Dornheim.

At least 127 records · Page 7Linked to original sources

arXiv2021

Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas

The \emph{ab initio} path integral Monte Carlo (PIMC) approach is one of the most successful methods in quantum many-body theory. A particular strength of this method is its straightforward access to imaginary-time correlation functions (ITCF). For example, the well-known density-density ITCF $F(\mathbf{q},τ)$ allows one to estimate the linear response of a given system for all wave vectors $\mathbf{q}$ from a single simulation of the unperturbed system. Moreover, it constitutes the basis for the reconstruction of the dynamic structure factor $S(\mathbf{q},ω)$ -- a key quantity in state-of-the-art scattering experiments. In this work, we present analogous relations between the nonlinear density response in quadratic and cubic order of the perturbation strength and generalized ITCFs measuring correlations between up to four imaginary-time arguments. As a practical demonstration of our new approach, we carry out simulations of the warm dense electron gas and find excellent agreement with previous PIMC results that had been obtained with substantially larger computational effort. In addition, we give a relation between a cubic ITCF and the triple dynamic structure factor $S(\mathbf{q}_1,ω_1;\mathbf{q}_2,ω_2)$, which evokes the enticing possibility to study dynamic three-body effects on an \emph{ab initio} level.

cond-mat.stat-mech↗

arXiv2021

Momentum distribution of the Uniform Electron Gas at finite temperature: Effects of spin-polarization

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization $ξ$. This allows us to unambiguously quantify the impact of spin-effects on the momentum distribution function $n(\mathbf{k})$ and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state $n(\mathbf{0})$ substantially depend on $ξ$. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of new methods and applications.

physics.comp-ph↗

arXiv2021

Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble

We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We find that the sign problem in the GCE is even more severe than in the canonical ensemble at the same conditions, which, in general, makes the latter the preferred option. Despite these difficulties, we show that fermionic PIMC simulations in the GCE are still feasible in many cases, which potentially gives access to important quantities like the compressiblity or the Matsubara Greens function. This has important implications for contemporary fields of research such as warm dense matter, ultracold atoms, and electrons in quantum dots.

physics.comp-ph↗

arXiv2021

A Machine-Learning Surrogate Model for ab initio Electronic Correlations at Extreme Conditions

The electronic structure in matter under extreme conditions is a challenging complex system prevalent in astrophysical objects and highly relevant for technological applications. We show how machine-learning surrogates in terms of neural networks have a profound impact on the efficient modeling of matter under extreme conditions. We demonstrate the utility of a surrogate model that is trained on \emph{ab initio} quantum Monte Carlo data for various applications in the emerging field of warm dense matter research.

physics.comp-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↗

arXiv2021

Momentum distribution function and short-range correlations of the warm dense electron gas -- ab initio quantum Monte Carlo results

In a classical plasma the momentum distribution, $n(k)$, decays exponentially, for large $k$, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, $n_\infty(k)\sim k^{-8}$ has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive \textit{ab initio} results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the $k^{-8}$ asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e. the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.

physics.plasm-ph↗

arXiv2021

Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation

The description of electronic exchange--correlation effects is of paramount importance for many applications in physics, chemistry, and beyond. In a recent Letter, Dornheim \textit{et al.} [\textit{Phys. Rev. Lett.}~\textbf{125}, 235001 (2020)] have presented the \emph{effective static approximation} (ESA) to the local field correction (LFC), which allows for the highly accurate estimation of electronic properties such as the interaction energy and the static structure factor. In the present work, we give an analytical parametrization of the LFC within ESA that is valid for any wave number, and available for the entire range of densities ($0.7\leq r_s \leq20$) and temperatures ($0\leq θ\leq 4$) that are relevant for applications both in the ground state and in the warm dense matter regime. A short implementation in Python is provided, which can easily be incorporated into existing codes. In addition, we present an extensive analysis of the performance of ESA regarding the estimation of various quantities like the dynamic structure factor, static dielectric function, the electronically screened ion-potential, and also stopping power in electronic medium. In summary, we find that the ESA gives an excellent description of all these quantities in the warm dense matter regime, and only becomes inaccurate when the electrons start to form a strongly correlated electron liquid ($r_s\sim20$). Moreover, we note that the exact incorporation of exact asymptotic limits often leads to a superior accuracy compared to the neural-net representation of the static LFC [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)].

physics.plasm-ph↗

arXiv2021

Overcoming finite-size effects in electronic structure simulations at extreme conditions

\textit{Ab initio} quantum Monte Carlo (QMC) methods in principle allow for the calculation of exact properties of correlated many-electron systems, but are in general limited to the simulation of a finite number of electrons $N$ in periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas (UEG) at finite temperature as it is relevant to contemporary research e.g. in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor $S(q)$ and in the interaction energy $v$, which is based on the density response formalism. We demonstrate that this method often allows to obtain $v$ in the TDL within a relative accuracy of $\sim0.2\%$ from as few as $N=4$ electrons without any empirical choices or knowledge of results for other values of $N$. Finally, we evaluate the applicability of our method upon increasing the density parameter $r_s$ and decreasing the temperature $T$.

cond-mat.stat-mech↗

arXiv2021

First-principles modeling of plasmons in aluminum under ambient and extreme conditions

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear-response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

cond-mat.mtrl-sci↗

arXiv2020

Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte-Carlo simulations

We systematically investigate finite-size effects in the dynamic structure factor $S(q,ω)$ of the uniform electron gas obtained via the analytic continuation of \textit{ab initio} path integral Monte-Carlo (PIMC) data for the imaginary-time density--density correlation function $F(q,τ)$. Using the recent scheme by Dornheim \textit{et al.}~[PRL \textbf{121}, 255001 (2018)], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as $N=14$ electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.

cond-mat.str-el↗

arXiv2020

Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory

We present an \emph{Effective Static Approximation} (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor $S(q,ω)$, the static structure factor $S(q)$, and the interaction energy $v$. The ESA combines the recent neural-net representation [\textit{J. Chem. Phys.} \textbf{151}, 194104 (2019)] of the temperature dependent LFC in the exact static limit with a consistent large wave-number limit obtained from Quantum Monte-Carlo data of the on-top pair distribution function $g(0)$. It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by re-evaluating the results of the recent {X-ray Thomson scattering experiment on aluminum} by Sperling \textit{et al.}~[\textit{Phys. Rev. Lett.} \textbf{115}, 115001 (2015)]. We find that an accurate incorporation of electronic correlations {in terms of the ESA} leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.

physics.plasm-ph↗

arXiv2020

Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration

Accurate thermodynamic simulations of correlated fermions using path integral Monte Carlo (PIMC) methods are of paramount importance for many applications such as the description of ultracold atoms, electrons in quantum dots, and warm-dense matter. The main obstacle is the fermion sign problem (FSP), which leads to an exponential increase in computation time both with increasing the system-size and with decreasing temperature. Very recently, Hirshberg et al. [J. Chem. Phys. 152, 171102 (2020)] have proposed to alleviate the FSP based on the Bogoliubov inequality. In the present work, we extend this approach by adding a parameter that controls the perturbation, allowing for an extrapolation to the exact result. In this way, we can also use thermodynamic integration to obtain an improved estimate of the fermionic energy. As a test system, we choose electrons in 2D and 3D quantum dots and find in some cases a speed-up exceeding 10^6 , as compared to standard PIMC, while retaining a relative accuracy of $\sim0.1\%$. Our approach is quite general and can readily be adapted to other simulation methods.

physics.comp-ph↗

arXiv2020

Screening of a test charge in a free-electron gas at warm dense matter and dense non-ideal plasma conditions

The screening of a test charge by partially degenerate non-ideal free electrons at conditions related to warm dense matter and dense plasmas is investigated using linear response theory and the local field correction based on ab inito Quantum Monte-Carlo simulations data. The analysis of the obtained results is performed by comparing to the random phase approximation and the Singwi-Tosi-Land-Sjölander approximation. The applicability of the long-wavelength approximation for the description of screening is investigated. The impact of electronic exchange-correlations effects on structural properties and the applicability of the screened potential from linear response theory for the simulation of the dynamics of ions are discussed.

physics.plasm-ph↗

arXiv2020

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,ω)$ and the plasmon dispersion $ω(q)$. Recently the first \textit{ab initio} results for $S(q,ω)$ of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations, [Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeros of the dielectric function can solve this problem for WDM conditions.

physics.plasm-ph↗

arXiv2020

Dynamic properties of the warm dense electron gas: an ab initio path integral Monte Carlo approach

There is growing interest in warm dense matter (WDM) -- an exotic state on the border between condensed matter and plasmas. Due to the simultaneous importance of quantum and correlation effects WDM is complicated to treat theoretically. A key role has been played by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, and recently extensive results for thermodynamic quantities have been obtained. The first extension of PIMC simulations to the dynamic structure factor of the uniform electron gas were reported by Dornheim \textit{et al.} [Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. This was based on an accurate reconstruction of the dynamic local field correction. Here we extend this concept to other dynamical quantities of the warm dense electron gas including the dynamic susceptibility, the dielectric function and the conductivity.

physics.comp-ph↗

arXiv2020

Ab initio Path Integral Monte Carlo Simulations of Quantum Dipole Systems in Traps: Superfluidity, Quantum Statistics, and Structural Properties

We present extensive \textit{ab initio} path integral Monte Carlo (PIMC) simulations of two-dimensional quantum dipole systems in a harmonic confinement, taking into account both Bose- and Fermi-statistics. This allows us to study the nonclassical rotational inertia, which can lead to a negative superfluid fraction in the case of fermions [Phys. Rev. Lett. \textbf{112}, 235301 (2014)]. Moreover, we study in detail the structural characteristics of such systems, and are able to clearly resolve the impact of quantum statistics on density profiles and the respective shell structure. Further, we present results for a more advanced center-two particle correlation function [Phys. Rev. E \textbf{91}, 043104 (2015)], which allows to detect differences between Fermi- and Bose-systems that do not manifest in other observables like the density. Overall, we find that bosonic systems sensitively react to even small values of the dipole--dipole coupling strength, whereas such a weak interaction is effectively masked for fermions by the Pauli exclusion principle. In addition, the abnormal superfluid fraction for fermions is not reflected by the structural properties of the system, which are equal to the bosonic case even though the moments of inertia diverge from each other. Lastly, we have demonstrated that fermionic PIMC simulations of quantum dipole systems are feasible despite the notorious fermion sign problem, which opens up new avenues for future investigations in this field.

physics.comp-ph↗

arXiv2020

Influence of finite temperature Exchange-Correlation effects in Hydrogen

We use density functional molecular dynamics (DFT-MD) to study the effect of finite temperature exchange-correlation (xc) in Hydrogen. Using the Kohn-Sham approach, the xc energy of the system, $E_{xc}(r_{s})$ is replaced by the xc free energy $f_{xc}(r_{s},Θ)$ within the local density approximation (LDA) based on parametrized path integral Monte Carlo (PIMC) data for the uniform electron gas (UEG) at warm dense matter (WDM) conditions. We observe insignificant changes in the equation of state (EOS) at the region of metal-insulator transition compared to the regular LDA form, whereas significant changes are observed for T$>$10000 K, i.e., in the important WDM regime. Thus, our results further corroborate the need for temperature-dependent xc functionals for DFT simulations of WDM systems. Moreover, we present the first finite-temperature DFT results for the EOS of Hydrogen in the electron liquid regime up to $r_{s}=14$ and find a drastic impact (about $20\%$) of thermal xc effects, which manifests at lower temperatures compared to WDM. We expect our results to be important for many applications beyond DFT, like quantum hydrodynamics and astrophysical models.

cond-mat.mtrl-sci↗