arXiv subjects

Jan Vorberger

Publications and source records attributed to Jan Vorberger.

At least 109 records · Page 6Linked to original sources

arXiv2022

Energy relaxation and electron-phonon coupling in laser-excited metals

The rate of energy transfer between electrons and phonons is investigated by a first principles framework for electron temperatures up to $T_e=50000$ K while considering the lattice at ground state. Two typical but differently complex metals are investigated, namely Aluminium and Copper. In order to reasonably take the electronic excitation effect into account, we adopt finite temperature density functional theory and linear response to determine the electron-temperature-dependent Eliashberg function and electron density of states. Of the three branch-dependent electron-phonon coupling strengths, the longitudinal acoustic mode plays a dominant role in the electron-phonon coupling for Aluminium for all temperatures considered here, but for Copper it only dominates above an electron temperature of $T_e=40000$ K. The second moment of the Eliashberg function and the electron phonon coupling constant at room temperature $T_e=315$ K show good agreement with other results. For increasing electron temperatures, we show the limits of the $T=0$ approximation for the Eliashberg function. Our present work provides a rich perspective on the phonon dynamics and this will help to improve insight into the underlying mechanism of energy flow in ultra-fast laser-metal interaction.

cond-mat.other↗

arXiv2022

The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\leqθ=k_\textnormal{B}T/E_\textnormal{F}\leq128$. This allows us to study the convergence of different properties towards the classical limit. In particular, we investigate the classical relation between the static structure factor $S(\mathbf{q})$ and the static local field correction $G(\mathbf{q})$, which is only fulfilled at low densities. Moreover, we compare our new results for the interaction energy to the parametrization of the UEG by Groth \emph{et al.}~[PRL \textbf{119}, 135001 (2017)], which interpolates between PIMC results for $θ\leq8$ and the Debye-Hückel limit, and to higher order analytical virial expansions. Finally, we consider the momentum distribution function $n(\mathbf{q})$ and find an interaction-induced increase in the occupation of the zero-momentum state even for $θ\gtrsim32$. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods.

physics.plasm-ph↗

arXiv2022

Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes

We explore a new formalism to study the nonlinear electronic density response based on Kohn-Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wave-numbers $q<2q_F$, with $q_F$ being the Fermi wave-number. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the non-linear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)].

physics.plasm-ph↗

arXiv2021

Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling

We present extensive new ab initio path integral Monte Carlo (PIMC) results for an electron gas at warm dense matter conditions that is subject to multiple harmonic perturbations. In addition to the previously investigated nonlinear effects at the original wave number [Dornheim \emph{et al.}, PRL \textbf{125}, 085001 (2020)] and the excitation of higher harmonics [Dornheim \emph{et al.}, PRR \textbf{3}, 033231 (2021)], the presence of multiple external potentials leads to mode-coupling effects, which constitute the dominant nonlinear effect and lead to a substantially more complicated density response compared to linear response theory. One possibility to estimate mode-coupling effects from a PIMC simulation of the unperturbed system is given in terms of generalized imaginary-time correlation functions that have been recently introduced by Dornheim \emph{et al.}~[JCP \textbf{155}, 054110 (2021)]. In addition, we extend our previous analytical theory of the nonlinear density response of the electron gas in terms of the static local field correction [Dornheim \emph{et al.}, PRL \textbf{125}, 235001 (2020)], which allows for a highly accurate description of the PIMC results with negligible computational cost.

physics.plasm-ph↗

arXiv2021

Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions

Warm dense matter is a highly active research area both at the frontier and interface of material science and plasma physics. We assess the performance of commonly used exchange-correlation (XC) approximation (LDA, PBE, PBEsol, and AM05) in the spin-polarized inhomogeneous electron gas under warm dense conditions based on exact path-integral quantum Monte-Carlo calculations. This extends our recent analysis on the relevance of inhomogeneities in the spin-unpolarized warm dense electron gas [Z.~Moldabekov et al., J. Chem. Phys. 155, 124116 (2021)]. We demonstrate that the predictive accuracy of these XC functionals deteriorates with (1) a decrease in density (corresponding to an increase in the inter-electronic correlation strength) and (2) an increase of the characteristic wave number of the density perturbation. We provide recommendations for the applicability of the considered XC functionals at conditions typical for warm dense matter. Furthermore, we hint at future possibilities for constructing more accurate XC functionals under these conditions.

physics.plasm-ph↗

arXiv2021

Path Integral Monte Carlo Simulations of liquid $^3$He without Fixed Nodes: Structural Properties and Collective Excitations

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of normal liquid $^3$He without any nodal constraints. This allows us to study the effects of temperature on different structural properties like the static structure factor $S(\mathbf{q})$, the momentum distribution $n(\mathbf{q})$, and the static density response function $χ(\mathbf{q})$, and to unambiguously quantify the impact of Fermi statistics. In addition, the dynamic structure factor $S(\mathbf{q},ω)$ is rigorously reconstructed from imaginary-time PIMC data, and we find the familiar phonon-maxon-roton dispersion that is well known from $^4$He and has been reported previously for two-dimensional $^3$He films [Nature \textbf{483}, 576-579 (2012)]. The comparison of our new results for both $S(\mathbf{q})$ and $S(\mathbf{q},ω)$ to neutron scattering measurements reveals an excellent agreement between theory and experiment.

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

Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

In a recent letter [\textit{Phys.~Rev.~Lett.}~\textbf{125}, 085001 (2020)], Dornheim \textit{et al.}~have presented the first \textit{ab initio} path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/four-body correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange-correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities ($r_s=0.5,\dots,10$) and temperatures ($θ=0.01,\dots,4$). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe three- and potentially even four-body correlation functions in WDM.

physics.plasm-ph↗

arXiv2021

Nonlinear electronic density response of the ferromagnetic uniform electron gas at warm dense matter conditions

In a recent Letter [T.~Dornheim \emph{et al.}, Phys.~Rev.~Lett.~\textbf{125}, 085001 (2020)], we have presented the first \emph{ab initio} results for the nonlinear density response of electrons in the warm dense matter regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo (PIMC) simulations of a \emph{ferromagnetic} electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin-effects on the nonlinear density response of the warm dense electron gas. In addition to their utility for the description of warm dense matter in an external magnetic field, our results further advance our current understanding of the uniform electron gas as a fundamental model system, which is important in its own right.

physics.plasm-ph↗

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

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

Lattice dynamics and ultrafast energy flow between electrons, spins, and phonons in a 3d ferromagnet

The ultrafast dynamics of magnetic order in a ferromagnet are governed by the interplay between electronic, magnetic and lattice degrees of freedom. In order to obtain a microscopic understanding of ultrafast demagnetization, information on the response of all three subsystems is required. A consistent description of demagnetization and microscopic energy flow, however, is still missing. Here, we combine a femtosecond electron diffraction study of the ultrafast lattice response of nickel to laser excitation with ab initio calculations of the electron-phonon interaction and energy-conserving atomistic spin dynamics simulations. Our model is in agreement with the observed lattice dynamics and previously reported electron and magnetization dynamics. Our approach reveals that the spin system is the dominating heat sink in the initial few hundreds of femtoseconds and implies a transient non-thermal state of the spins. Our results provide a clear picture of the microscopic energy flow between electronic, magnetic and lattice degrees of freedom on ultrafast timescales and constitute a foundation for theoretical descriptions of demagnetization that are consistent with the dynamics of all three subsystems.

cond-mat.mtrl-sci↗

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↗