arXiv subjects

Panagiotis Tolias

Publications and source records attributed to Panagiotis Tolias.

48 records · Page 3Linked to original sources

arXiv2023

Ab initio path integral Monte Carlo simulations of the uniform electron gas on large length scales

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, material science, and related disciplines. At finite temperatures, the gold standard is given by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, which do not require any empirical input, but exhibit an exponential increase in the required compute time for fermionic systems with increasing the system size $N$. Very recently, it has been suggested to compute fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles. In the present work, we use this technique to carry out very large ($N\leq1000$) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of investigated properties, i.e., the static structure factor, the static density response function, and local field correction, over the entire range of length scales.

physics.chem-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

Wall cratering upon high velocity normal dust impact

Dust-wall high speed impacts, triggered by the termination of runaway electrons on plasma facing components, constitute a source of erosion. Normal high velocity mechanical impacts of tungsten dust on bulk tungsten plates are reproduced in a controlled manner by light gas gun shooting systems. Post-mortem surface analysis revealed that three erosion regimes are realized; plastic deformation, bonding and partial disintegration. The large impact statistics allowed the extraction of reliable empirical damage laws in the latter regime, which can be employed for erosion estimates in future reactors.

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

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

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

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

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

Spin-resolved density response of the warm dense electron gas

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the spin-resolved density response of the uniform electron gas (UEG) at warm dense matter conditions. This allows us to unambiguously assess the accuracy of previous theoretical approximations, thereby providing valuable new insights for the future development of dielectric schemes. From a physical perspective, we observe a nontrivial manifestation of an effective electron--electron attraction that emerges in the spin-offdiagonal static density response function at strong coupling, $r_s\gtrsim5$. All PIMC results are freely available online and can be used to benchmark new approximations and simulation schemes.

physics.comp-ph↗

arXiv2022

Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations

The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair potentials that take into account the effects of the complex many-body medium consistently. In this work, we present extensive, highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) results for the effective interaction and the effective force between two electrons in the presence of the uniform electron gas (UEG). This gives us a direct insight into finite-size effects, thereby opening up the possibility for novel domain decompositions and methodological advances. In addition, we present unassailable numerical proof for an effective attraction between two electrons under moderate coupling conditions, without the mediation of an underlying ionic structure. Finally, we compare our exact PIMC results to effective potentials from linear-response theory, and we demonstrate their usefulness for the description of the dynamic structure factor. All PIMC results are made freely available online and can be used as a thorough benchmark for new developments and approximations.

physics.comp-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↗