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

Abstract

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\le \theta =k_{\text{B}}T/E_{\text{F}}\le 128$. 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 $\theta \le 8$ 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 $\theta \gtrsim 32$. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods.

References in corpus (64)

• Perspective on density functional theory
• A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• The Uniform Electron Gas at Warm Dense Matter Conditions
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• Local Spin-density Approximation Exchange-correlation Free-energy Functional
• FPEOS: A First-Principles Equation of State Table of Deuterium for Inertial Confinement Fusion Applications
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Finite-size errors in continuum quantum Monte Carlo calculations
• Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
• Ab initio simulation of warm dense matter
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• \textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter
• The importance of finite-temperature exchange-correlation for warm dense matter calculations
• Ab initio thermodynamic results for the degenerate electron gas at finite temperature
• Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas
• The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter
• Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
• Accurate exchange-correlation energies for the warm dense electron gas
• The Static Local Field Correction of the Warm Dense Electron Gas: An ab Initio Path Integral Monte Carlo Study and Machine Learning Representation
• Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory
• Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas
• Nonlinear Electronic Density Response in Warm Dense Matter
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes
• Uniform electron gas at finite temperatures
• Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature
• The momentum distribution of the homogeneous electron gas
• \emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas
• Influence of finite temperature Exchange-Correlation effects in Hydrogen
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation
• Dynamic properties of the warm dense electron gas: an ab initio path integral Monte Carlo approach
• The Strongly Coupled Electron Liquid: ab initio Path Integral Monte Carlo Simulations and Dielectric Theories
• Structural characteristics of strongly coupled ions in a dense quantum plasma
• Path Integral Monte Carlo Simulation of Degenerate Electrons: Permutation-Cycle Properties
• Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas
• Permutation Blocking Path Integral Monte Carlo approach to the Static Density Response of the Warm Dense Electron Gas
• Ab initio results for the plasmon dispersion and damping of the warm dense electron gas
• Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Nonlinear density response from imaginary-time correlation functions: Ab initio path integral Monte Carlo simulations of the warm dense electron gas
• Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte-Carlo simulations
• Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature without fixed nodes
• Restricted configuration path integral Monte Carlo
• Dynamical structure factor of strongly coupled ions in a dense quantum plasma
• Effective Field Theory for Highly Ionized Plasmas
• Overcoming finite-size effects in electronic structure simulations at extreme conditions
• \textit{Ab Initio} results for the Static Structure Factor of the Warm Dense Electron Gas
• Lowering of the Kinetic Energy in Interacting Quantum Systems
• Ab initio path integral Monte Carlo simulation of the Uniform Electron Gas in the High Energy Density Regime
• Momentum distribution function and short-range correlations of the warm dense electron gas -- ab initio quantum Monte Carlo results
• Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble
• Integral equation theory based dielectric scheme for strongly coupled electron liquids
• The Radius of PSR J0740+6620 from NICER and XMM-Newton Data
• Classical bridge functions in classical and quantum plasma liquids
• Classical Representation of a Quantum System at Equilibrium: Theory
• Classical Representation of a Quantum System at Equilibrium: Applications
• Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter
• Gravity mode offset and properties of the evanescent zone in red-giant stars
• Thermal Signals from Collective Electronic Excitations in Inhomogeneous Warm Dense Matter

Cited by in corpus (7)

• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Virial coefficients of the Uniform Electron Gas from Path Integral Monte Carlo Simulations
• Energy response and spatial alignment of the perturbed electron gas
• The virial expansion of the Hydrogen equation of state in comparison to PIMC simulations: the quasiparticle concept, IPD, and ionization degree