Extremal properties of the Harris-Foulkes functional and an improved screening calculation for the electron gas

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

The 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 simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the sign problem. Here, 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 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 uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 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).

Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations

Rigorous diagnostics of experiments with warm dense matter are notoriously difficult. A key method is X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [Nat. Commun. 13, 7911 (2022)] introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions. On the one hand, switching from the frequency to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without relying on any models or approximations. On the other hand, the bulk of theoretical work in dynamic quantum many-body theory is devoted to the frequency domain, and, to the best of our knowledge, the manifestation of physics properties within the imaginary-time density-density correlation function (ITCF) remains poorly understood. In the present work, we aim to fill this gap by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wavenumbers, densities and temperatures. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

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(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(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 methods and applications.

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

We present an 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 by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] 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 reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. 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.

Nonlinear Electronic Density Response in Warm Dense Matter

Warm dense matter (WDM)-an extreme state with high temperatures and densities that occurs, e.g., in astrophysical objects-constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first ab initio path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.

Computing the self-consistent field in Kohn-Sham density functional theory

A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory (DFT). The aims of this work are two-fold. First, we explore the properties of Kohn-Sham DFT as it pertains to the convergence of self-consistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the scf-x _n suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner.

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.

A viscous quantum hydrodynamics model based on dynamic density functional theory

Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.

Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.156403], we presented the first quantum Monte Carlo (QMC) results for the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below θ=k_{B}T/E_{F}=0.5 and (ii) QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first completely ab initio exchange-correlation free energy functional; the accuracy achieved is an unprecedented ∼0.3%. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas

The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)10.1088/1367-2630/17/7/073017] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows us to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.

LDA and GGA Investigations of Some Ground-State Properties and the Compton Profile of Copper with the All-Electron MAPW Method

The electronic structure is self-consistently evaluated both in the local-density and the generalized-gradient approximations. The convergence with respect to the intrinsic parameters of the modified augmented plane-wave scheme is thoroughly investigated. Besides the Ar-core, the less-extended Ne-core and the most appropriate exchange-correlations functionals are considered. It is studied how some characteristic ground-state properties and the Compton profiles depend on these choices. Apart from the long wave limit of the Compton profiles, most of the other properties are found in good agreement with the experimental facts.

Plasmons in strongly coupled shock-compressed matter

We present the first measurements of the plasmon dispersion and damping in laser shock-compressed solid matter. Petawatt laser produced K-α radiation scatters on boron targets compressed by a 10 ns-long 400 J laser pulse. In the vicinity of the Fermi momentum, the scattering spectra show dispersionless, collisionally damped plasmons, indicating a strongly coupled electron liquid. These observations agree with calculations that include the Born-Mermin approximation to account for electron-ion collisional damping and local field corrections reflecting electron-electron correlations.

Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas

The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters r(s). These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.

Study of superconducting state parameters of ternary metallic glasses through pseudopotential approach

A theoretical investigation on the screening dependence of the superconducting state parameters (SSPs) viz. the electron-phonon coupling strength λ, the Coulomb pseudopotential μ∗, the transition temperature T_C, the isotope effect exponent α and the effective interaction strength N₀V of some ternary metallic glasses such as Ti₅₀Be₃₄Zr₁₀, (Mo_0.6Ru_0.4)₇₈B₂₂, (Mo_0.6Ru_0.4)₈₀B₂₀, (Mo_0.4Ru_0.6)₈₀P₂₀, (Mo_0.6Ru_0.4)₇₀Si₃₀, (Mo_0.6Ru_0.4)₈₄B₁₆, (Mo_0.6Ru_0.4)₇₂Si₂₈, (Mo_0.6Ru_0.4)₈₆B₁₄, (Mo_0.6Ru_0.4)₇₆Si₂₄, (Mo_0.6Ru_0.4)₇₈Si₂₂, (Mo_0.6Ru_0.4)₈₀Si₂₀, (Mo_0.6Ru_0.4)₈₂Si₁₈ and (Mo_0.6Ru_0.4)₈₀P₂₀ is reported for the first time using Ashcroft's empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al (F) and Sarkar et al (S) are used in the present investigation to study the effect of screening on the aforesaid properties. It is observed that λ and T_C are reasonably sensitive to the selection of the local field correction functions, whereas μ∗, α and N₀V show weak dependences on the local field correction functions. The transition temperature T_C obtained from the H-local field correction function is found to be in excellent agreement with available experimental data. Also, the present results are found to be in qualitative agreement with other earlier reported data, which confirms the existence of the superconducting phase in the above ternary metallic glasses.

Density functional theory of complex transition densities

We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.

Excess entropy scaling for the diffusion coefficient in expanded liquid metals

Molecular-dynamics simulation is used to compute the pair correlation function and the velocity autocorrelation function of Cs and Rb along the liquid-vapor coexistence curve, from which the excess entropy S(ex) and the diffusion coefficient D are deduced. The numerical results of both physical properties are correlated and a scaling law between the excess entropy and the reduced diffusion coefficient D(*)(=D/D(0)) is investigated for different expressions of the reduction parameter D(0). The choice of thermodynamic states along the liquid--vapor coexistence curve gives us the possibility to extend the investigation of the relation between the reduced diffusion coefficient and the excess entropy over a wide area and to test the adequacy of the scaling law confidently.

Accurate total energies without self-consistency

We present a new way of calculating approximate but accurate total energies within the framework of density functional theory. Our technique is based on an expansion of the energy functional to second order and does not require self-consistent iterations of the total density. The functional can be minimized by using the same techniques as developed for variational density functional perturbation theory. The method is ideally suited to systems composed of weakly interacting fragments, but it can also be applied to semiconductors and insulators. We show the versatility of our approach in a variety of examples exhibiting different types of chemical bonding.

Stopping power of strongly coupled electronic plasmas: sum rules and asymptotic forms

The stopping power of coupled electronic plasmas is investigated. Within the dielectric formalism and employing the method of frequency moments for the dielectric function we obtain a general formula describing the linear stopping power of a coupled plasma. Analytical results for the low- and high-projectile-velocity asymptotic forms are obtained. A sum rule for the plasma heavy ions linear stopping power projectile velocity distribution is established to be related to the dielectric permeability "negative" frequency moment. This permits for a simple interpretation of stopping power data.

Ultra-high Resolution Compton Scattering of Li Metal: Evaluation with Respect to the Correlation Corrected Occupation Number Density

Directional Compton profiles of Li metal measured with ultra-high momentum space resolution (0.02 a.u.) were analysed in terms of their reciprocal form factors

Simple classical mapping of the spin-polarized quantum electron gas: distribution functions and local-field corrections

We use the now well known spin unpolarized exchange-correlation energy E(xc) of the uniform electron gas as the basic "many-body" input to determine the temperature T(q) of a classical Coulomb fluid having the same correlation energy as the quantum system. It is shown that the spin-polarized pair distribution functions (SPDFs) of the classical fluid at T(q), obtained using the hypernetted chain equation, are in excellent agreement with those of the T = 0 quantum fluid obtained by quantum Monte Carlo (QMC) simulations. These methods are computationally simple and easily applied to problems which are currently beyond QMC simulations. Results are presented for the SPDFs and the local-field corrections to the response functions of the electron fluid at T = 0 and finite T.