arXiv subjects

Zhandos A. Moldabekov

Publications and source records attributed to Zhandos A. Moldabekov.

At least 19 recordsLinked to original sources

arXiv2026

The quadratic density response function for non-interacting fermions at arbitrary temperature

We develop and implement the quadratic density response function of non-interacting fermions at arbitrary temperature, frequencies, and wave vectors. Starting from a Green's function formulation, we derive the quadratic response and demonstrate its equivalence to the result obtained from the Wigner equation. We further derive the classical limit through a perturbative expansion of the Vlasov equation and demonstrate that the quantum and classical formulations agree in the high-temperature limit. We analyse the limiting behaviour with respect to wavenumber and derive the zeroth harmonic response. Two independent implementations are provided and extensively benchmarked against density-functional theory, canonical path integral Monte Carlo (PIMC), and grand canonical PIMC simulations. As the density response of the interacting electron gas is commonly modelled through the ideal response functions and approximate models for the local field correction, the presented formulation will also allow for more complete explorations of interacting systems. Especially, our efficient implementation, which evaluates the ideal static and dynamic quadratic response functions in less than 0.5 ms on a 1.3 GHz processor, will enable evaluation of quadratic corrections to integrated quantities such as interaction potentials and stopping powers in warm dense matter.

physics.plasm-ph↗

arXiv2026

Nonempirical Time-Dependent Density Functional Theory Framework for Nonlocal Exchange--Correlation Potentials

Advanced, orbital-dependent exchange--correlation (XC) functionals can significantly improve the description of electronic structural properties, but they substantially worsen spectral properties that are computed within standard linear-response time-dependent density functional theory frameworks. This is not a failure of the underlying Kohn-Sham states, but due to a formal inconsistency in the treatment of the dynamic density response when the non-locality of the XC potential is not taken into account consistently on the level of the full off-diagonal density matrix. To avoid these complexities, we present a non-empirical additive correction $Δf_\textnormal{xc}(\mathbf{q},ω)$ to the dynamic XC kernel that re-enforces the exact f-sum rule of the non-local KS Hamiltonian within TDDFT. Comparing our new results against a representative set of accurate experimental measurements (ambient aluminum, silicon and carbon, as well as heated and compressed aluminum) reveals a dramatic improvement in all cases without any additional computational cost. The corresponding extension to the open-source GPAW code is made freely available online. We further investigate the implications of non-local pseudopotentials and show that the non-locality has an important, physically motivated effect that is indispensable to capture the correct plasmon dispersion in lieu of full all-electron simulations. In addition to being important for the estimation of a plethora of dynamic and spectral properties, our work constitutes an important step towards a universal XC functional that can be used to estimate all kinds of observables with high accuracy. Finally, we outline the potential utility of our framework for the development of advanced non-local XC functionals, and suggest a new way to rigorously verify non-local pseudopotentials against experimental measurements of collective excitations.

cond-mat.mtrl-sci↗

arXiv2026

Reconciling chemical models of X-ray Thomson Scattering with the Bethe $f$-sum rule

X-ray Thomson scattering (XRTS) is a key diagnostic for high-energy-density plasmas, which can exhibit significant quantum effects even at elevated temperatures. XRTS experiments are commonly interpreted using the Chihara decomposition, that was derived in the chemical picture and, thus, separates contributions from bound and free electrons. Despite being the de-facto standard for analysing measurements, a well-known shortcoming is that the standard bound-state treatment in the form of the impulse approximation fails to satisfy fundamental theoretical constraints, most notably the Bethe $f$-sum rule (BFSR). The problem arises due to the usage of plane waves in the impulse approximation as well as non-negligible contributions from bound-bound transitions. In this work, we present a minimal analytical extension of the Chihara decomposition of the dynamic structure factor for matter in the ground state, using hydrogenic bound-free and bound-bound transitions. We demonstrate that compliance with the BFSR is only achieved when both bound-bound transitions are explicitly included and an exact treatment of the bound-free contribution is applied. Finally, detector ray-tracing simulations for atomic hydrogen demonstrate experimentally detectable deviations from the standard Chihara model. The model will be made available in the open source XRTS library xDAVE [Bellenbaum et al., Phys. Plasmas (in print), arxiv:2604.27237].

physics.plasm-ph↗

arXiv2026

Ab initio path integral Monte Carlo study of the 2D uniform electron liquid at finite temperatures

We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the two-dimensional uniform electron gas (2DEG), covering a broad range of density parameters $r_s=0.1,\dots,50$ and temperatures $Θ=k_\textnormal{B}T/E_\textnormal{Fermi}=0.5,\dots,16$. This allows us to analyze various structural, linear density response and spectral properties. We find clear evidence of a \emph{roton-type} feature in the dynamic structure factor at strong coupling and intermediate wavenumbers. We also benchmark novel dielectric theory implementations for the 2DEG~[Kalkavouras \emph{et al.}~arXiv:2601.14989] for structural and spectral properties across the liquid phase diagram. The PIMC results can be used to benchmark existing theories and approximations, and guide the development of new methodologies.

cond-mat.quant-gas↗

arXiv2026

Thermal PBE in warm dense matter: Does it matter and is it accurate?

Conditional probability density functional theory has recently been used to derive the temperature dependence of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) for the exchange-correlation (XC) free energy. We implement and systematically benchmark thermal PBE within Kohn-Sham density functional theory calculations of warm dense matter. Comparisons with the local density approximation (LDA) and PBE functionals, as well as thermal LDA, show that thermal PBE significantly improves the description of warm dense matter properties, including energies, forces, pressures, and electronic charge densities. In particular, thermal PBE exhibits close agreement with path integral Monte Carlo (PIMC) reference data at negligible additional computational cost. This work demonstrates the practical utility of thermal PBE as an accurate semilocal functional for simulations in the warm dense regime.

cond-mat.mtrl-sci↗

arXiv2026

A Momentum-Resolved X-ray Thomson Scattering Benchmark of Electronic-Response Models in Warm Dense Aluminium

The robust diagnosis of conditions generated in warm dense matter (WDM) experiments remains a persistent challenge. Here we describe the measurement of shock-compressed aluminium at 50 GPa with angle-resolved femtosecond x-ray Thomson scattering (XRTS) over a wide range of scattering wavevectors at the European XFEL. The measured plasmon dispersion and line shape show that the de facto standard approach for analysing XRTS spectra, based on uniform-electron-gas models, systematically overestimates the resonance energy by up to 8 eV. We present an ab initio approach that agrees within the experimental uncertainty and demonstrates that accounting for shock-induced disorder is critical for interpreting shock-compressed systems, providing evidence that ab initio treatments are required for reliable XRTS inference in warm dense aluminium.

physics.plasm-ph↗

arXiv2026

Reweighting Estimators for Density Response in Path Integral Monte Carlo: Applications to linear, nonlinear and cross-species density response

We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed system are used to estimate the properties of a system perturbed by an external harmonic potential. This allows the linear and nonlinear static density response to be estimated purely from simulations of the unperturbed system. The method is demonstrated for the uniform electron gas under warm dense matter and strongly coupled conditions using ab initio path integral Monte Carlo simulations. The performance of the method with respect to the number of particles and the number of imaginary time slices is investigated. The scheme is generalised to consider multiple external perturbations, acting on different species and with different wavenumbers, giving one access to additional cross-species density response functions and the complete quadratic response function resolved for both wave number arguments through mode coupling. The flexibility of the methodology opens the possibility to investigate numerous new density response properties to further advance our understanding of interacting quantum many-body systems across a broad range of applications.

physics.chem-ph↗

arXiv2026

Enhancing the Efficiency of Time-Dependent Density Functional Theory Calculations of Dynamic Response Properties

X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density--density correlation function, which naturally emerges in Feynman's path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.

cond-mat.mtrl-sci↗

arXiv2026

Roadmap for warm dense matter physics

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations \& experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

physics.plasm-ph↗

arXiv2026

Generalized density functional theory framework for the non-linear density response of quantum many-body systems

A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to non-linear static density response functions in quantum many-body systems. Within this framework, explicit expressions are derived for various higher-order response functions of systems that are homogeneous on average, including the first theoretical result for the cubic response at the first harmonic $χ_0^{(1,3)}(\vec{q})$. Specifically, our framework includes hitherto neglected mode-coupling effects that are important for the non-linear density response even in the presence of a single harmonic perturbation. We compare these predictions for $χ_0^{(1,3)}(\vec{q})$ to new Kohn-Sham DFT simulations, leading to excellent agreement between theory and numerical results. Exact analytical expressions are also obtained for the long-wavelength limits of the ideal quadratic and cubic response functions. Particular emphasis is placed on the connections between the third- and fourth-order functional derivatives of the non-interacting free-energy functional $F_s[n]$ and the ideal quadratic and cubic response functions of the uniform electron gas, respectively. These relations provide exact constraints that may prove useful for the future construction of improved approximations to $F_s[n]$, in particular for warm dense matter applications at finite temperatures. Here, we use this framework to assess several commonly employed approximations to $F_s[n]$ through orbital-free DFT simulations of the harmonically perturbed ideal electron gas. The results are compared with Kohn-Sham DFT calculations across temperatures ranging from the ground state to the warm dense regime. Additionally, we analyze in detail the temperature- and wavenumber-dependent non-monotonic behavior of the ideal quadratic and cubic response functions.

cond-mat.stat-mech↗

arXiv2026

Unlocking the Power of Orbital-Free Density Functional Theory to Explore the Electronic Structure Under Extreme Conditions

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of the electronic structure under extreme pressures and temperatures, such as those encountered in stellar interiors and inertial confinement fusion experiments, challenging theoretical models for interpreting experimental data. Kohn-Sham density functional theory (KSDFT) has been successfully applied to analyze experimental X-ray scattering measurements, but its high computational cost renders routine application impractical. Orbital-free DFT (OFDFT) is a substantially more efficient alternative, with computational cost scaling linearly with system size and a weak temperature dependence, yet it often lacks the accuracy required for electronic structure description. Overcoming this limitation, we present a non-empirical Kohn-Sham-assisted orbital-free density functional framework for calculations at extreme conditions, which enables efficient OFDFT simulations with KSDFT-level accuracy for electron densities, electron-ion structure factors, and equations of state across a broad range of conditions. Benchmark comparisons with quantum Monte Carlo data for dense hydrogen and validation against Rayleigh weight measurements of hot dense beryllium demonstrate the reliability of the framework and speedups of up to several hundred times compared with KSDFT. We further show that even at temperatures on the order of 100 eV, quantum non-locality remains essential for correctly describing the electronic structure of dense hydrogen.

cond-mat.mtrl-sci↗

arXiv2025

Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations

Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense matter theory is given by thermal density functional theory (DFT), which, however, suffers from two limitations: (i) its accuracy can depend on the utilized exchange--correlation (XC) functional, which has to be approximated and (ii) it is generally limited to single-electron properties such as the density distribution. Here, we present a new ansatz combining time-dependent DFT results for the dynamic structure factor $S_{ee}(\mathbf{q},ω)$ with static DFT results for the density response. This allows us to estimate the electron--electron static structure factor $S_{ee}(\mathbf{q})$ of warm dense hydrogen with high accuracy over a broad range of densities and temperatures. In addition to its value for the study of warm dense matter, our work opens up new avenues for the future study of electronic correlations exclusively within the framework of DFT for a host of applications.

physics.plasm-ph↗

arXiv2025

Taylor series perspective on ab initio path integral Monte Carlo simulations with Fermi-Dirac statistics

The fermion sign problem constitutes a fundamental computational bottleneck across a plethora of research fields in physics, quantum chemistry and related disciplines. Recently, it has been suggested to alleviate the sign problem in \emph{ab initio} path integral Molecular Dynamics and path integral Monte Carlo (PIMC) calculations based on the simulation of fictitious identical particles that are represented by a continuous quantum statistics variable $ξ$ [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)]. This idea facilitated a host of applications including the interpretation of an x-ray scattering experiment with strongly compressed beryllium at the National Ignition Facility [\textit{Nature Commun.}~\textbf{16}, 5103 (2025)]. In the present work, we express the original isothermal $ξ$-extrapolation method as a special case of a truncated Taylor series expansion around the $ξ=0$ limit of distinguishable particles. We derive new PIMC estimators that allow us to evaluate the Taylor coefficients up to arbitrary order and we carry out extensive new PIMC simulations of the warm dense electron gas to systematically analyze the sign problem from this new perspective. This gives us important insights into the applicability of the $ξ$-extrapolation method for different levels of quantum degeneracy in terms of the Taylor series radius of convergence. Moreover, the direct PIMC evaluation of the $ξ$-derivatives, in principle, removes the necessity for simulations at different values of $ξ$ and can facilitate more efficient simulations that are designed to maximize compute time in those regions of the full permutation space that contribute most to the final Taylor estimate of the fermionic expectation value of interest.

physics.chem-ph↗

arXiv2025

Accelerated free energy estimation in ab initio path integral Monte Carlo simulations

We present a methodology for accelerating the estimation of the free energy from path integral Monte Carlo simulations by considering an intermediate artificial reference system where interactions are inexpensive to evaluate numerically. Using the spherically averaged Ewald interaction as this intermediate reference system for the uniform electron gas, the interaction contribution for the free energy was evaluated up to 18 times faster than the Ewald-only method. Furthermore, a $ξ$-extrapolation technique was tested and applied to alleviate the fermion sign problem and to resolve the sign for large particle numbers. Combining these two techniques enabled the evaluation of the free energy for a system of 1000 electrons, where both finite-size and statistical errors are below chemical accuracy. The general procedure can be applied to systems relevant for planetary and inertial confinement fusion modeling with low to moderate levels of quantum degeneracy.

physics.chem-ph↗

arXiv2025

Second roton feature in the strongly coupled electron liquid

We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) results for the dynamic properties of the finite temperature uniform electron gas (UEG) over a broad range of densities, $2\leq r_s\leq300$. We demonstrate that the direct analysis of the imaginary-time density--density correlation function (ITCF) allows for a rigorous assessment of the density and temperature dependence of the previously reported roton-type feature [T.~Dornheim, \emph{Phys.~Rev.~Lett.}~\textbf{121}, 255001 (2018)] at intermediate wavenumbers. We clearly resolve the emergence of a second roton at the second harmonic of the original feature for $r_s\gtrsim100$, which we identify as an incipient phonon dispersion. Finally, we use our highly accurate PIMC results for the ITCF as the basis for an analytic continuation to compute the dynamic structure factor, which additionally substantiates the existence of the second roton in the strongly coupled electron liquid. Our investigation further elucidates the complex interplay between quantum delocalization and Coulomb coupling in the UEG. All PIMC results are freely available online and provide valuable benchmarks for other theoretical methodologies and approximations.

physics.chem-ph↗

arXiv2025

Model-free Rayleigh weight from x-ray Thomson scattering measurements

X-ray Thomson scattering (XRTS) has emerged as a powerful tool for the diagnostics of matter under extreme conditions. In principle, it gives one access to important system parameters such as the temperature, density, and ionization state, but the interpretation of the measured XRTS intensity usually relies on theoretical models and approximations. In this work, we show that it is possible to extract the Rayleigh weight -- a key property that describes the electronic localization around the ions -- directly from the experimental data without the need for any model calculations or simulations. As a practical application, we consider an experimental measurement of strongly compressed Be at the National Ignition Facility (NIF) [Döppner \emph{et al.}, \textit{Nature} \textbf{618}, 270-275 (2023)]. In addition to being interesting in their own right, our results will open up new avenues for diagnostics from \emph{ab initio} simulations, help to further constrain existing chemical models, and constitute a rigorous benchmark for theory and simulations.

physics.plasm-ph↗

arXiv2025

Applying the Liouville-Lanczos Method of Time-Dependent Density-Functional Theory to Warm Dense Matter

Ab initio modeling of dynamic structure factors (DSF) and related density response properties in the warm dense matter (WDM) regime is a challenging computational task. The DSF, convolved with a probing X-ray beam and instrument function, is measured in X-ray Thomson scattering (XRTS) experiments, which allows for the study of electronic structure properties at the microscopic level. Among the various ab initio methods, linear response time-dependent density functional theory (LR-TDDFT) is a key framework for simulating the DSF. The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation. A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases, making LR-TDDFT impractical for modeling XRTS measurements over large energy scales, such as in backward scattering geometry. We consider and test an alternative approach that employs the Liouville-Lanczos (LL) method for simulating the DSF. This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed. We compare the results obtained from the LL method with those from the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen. Additionally, we utilize exact path integral Monte Carlo (PIMC) results for the imaginary-time density-density correlation function (ITCF) of warm dense hydrogen to rigorously benchmark the LL approach. We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers, the effects of pseudopotentials, and the role of Lorentzian smearing. The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape, supporting experimental efforts and advancing WDM theory.

physics.plasm-ph↗

arXiv2025

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on exact simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree -- quantities which are otherwise not directly accessible from the physical model -- from exact ab initio path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and non-equilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high density and high temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from exact quantum Monte Carlo simulations.

physics.chem-ph↗