Ab initio Density Response and Local Field Factor of Warm Dense Hydrogen

Ab initio Density Response and Local Field Factor of Warm Dense Hydrogen

13 Mar 2024 | Tobias Dornheim, Sebastian Schwalbe, Panagiotis Tolia, Maximilian P. Böhme, Zhandos A. Moldabekov, Jan Vorberger
This paper presents quasi-exact ab initio path integral Monte Carlo (PIMC) results for the partial static density responses and local field factors of hydrogen in the warm dense matter (WDM) regime, ranging from solid density to strongly compressed conditions. The full dynamic treatment of electrons and protons allows for a rigorous quantification of both electronic and ionic exchange-correlation effects, enabling comparisons with previous incomplete models such as the uniform electron gas and electrons in a fixed ion snapshot potential. The results are crucial for upcoming X-ray Thomson scattering (XRTS) experiments with hydrogen jets and fusion plasmas, as they provide unambiguous predictions for the density response of hydrogen. The PIMC results are freely available and can be used for various applications, including inertial confinement fusion calculations and modeling dense astrophysical objects. They also serve as valuable benchmark data for approximate but computationally less demanding approaches like density functional theory and PIMC within the fixed-node approximation. The study focuses on the linear density response of hydrogen, which is a key material property in WDM research. XRTS experiments are a key diagnostic tool for WDM, and the measured XRTS intensity provides access to the equation-of-state properties of the material, which are crucial for ICF applications and astrophysical modeling. However, the interpretation of XRTS intensity is often based on uncontrolled approximations, such as the Chihara decomposition, which can lead to uncertainties in inferred parameters like temperature, density, and ionization. The paper also discusses the importance of the local field factors in WDM theory, which are essential for calculating stopping power, electronic friction, electrical and thermal conductivities, opacity, ionization potential depression, and effective ion-ion potentials. Additionally, they are crucial for constructing advanced nonlocal exchange-correlation functionals for thermal DFT simulations. The study uses the PIMC method to simulate the behavior of hydrogen, treating electrons and protons dynamically on the same footing. This approach allows for the calculation of all components of the density response, including the electron-electron, electron-proton, and proton-proton local field factors. The results show that electronic localization around ions has significant implications for the interpretation of XRTS experiments, particularly at solid state densities, where the effects are significant over the entire relevant wavenumber range. The simulations are quasi-exact, with no fixed-node approximation imposed. To address the fermion sign problem, the results are obtained by averaging over a large number of Monte Carlo samples, making the simulations computationally expensive. The study also employs the recently introduced ξ-extrapolation method to access larger system sizes, and finds that finite-size effects are generally negligible at these conditions. The results provide a rigorous benchmark for computationally less costly but approximate approaches such as thermal DFT or PIMC within the fixed-node approximation. They also serve as direct predictions for upcoming XRTS experiments with hydrogen jets and ICF plasThis paper presents quasi-exact ab initio path integral Monte Carlo (PIMC) results for the partial static density responses and local field factors of hydrogen in the warm dense matter (WDM) regime, ranging from solid density to strongly compressed conditions. The full dynamic treatment of electrons and protons allows for a rigorous quantification of both electronic and ionic exchange-correlation effects, enabling comparisons with previous incomplete models such as the uniform electron gas and electrons in a fixed ion snapshot potential. The results are crucial for upcoming X-ray Thomson scattering (XRTS) experiments with hydrogen jets and fusion plasmas, as they provide unambiguous predictions for the density response of hydrogen. The PIMC results are freely available and can be used for various applications, including inertial confinement fusion calculations and modeling dense astrophysical objects. They also serve as valuable benchmark data for approximate but computationally less demanding approaches like density functional theory and PIMC within the fixed-node approximation. The study focuses on the linear density response of hydrogen, which is a key material property in WDM research. XRTS experiments are a key diagnostic tool for WDM, and the measured XRTS intensity provides access to the equation-of-state properties of the material, which are crucial for ICF applications and astrophysical modeling. However, the interpretation of XRTS intensity is often based on uncontrolled approximations, such as the Chihara decomposition, which can lead to uncertainties in inferred parameters like temperature, density, and ionization. The paper also discusses the importance of the local field factors in WDM theory, which are essential for calculating stopping power, electronic friction, electrical and thermal conductivities, opacity, ionization potential depression, and effective ion-ion potentials. Additionally, they are crucial for constructing advanced nonlocal exchange-correlation functionals for thermal DFT simulations. The study uses the PIMC method to simulate the behavior of hydrogen, treating electrons and protons dynamically on the same footing. This approach allows for the calculation of all components of the density response, including the electron-electron, electron-proton, and proton-proton local field factors. The results show that electronic localization around ions has significant implications for the interpretation of XRTS experiments, particularly at solid state densities, where the effects are significant over the entire relevant wavenumber range. The simulations are quasi-exact, with no fixed-node approximation imposed. To address the fermion sign problem, the results are obtained by averaging over a large number of Monte Carlo samples, making the simulations computationally expensive. The study also employs the recently introduced ξ-extrapolation method to access larger system sizes, and finds that finite-size effects are generally negligible at these conditions. The results provide a rigorous benchmark for computationally less costly but approximate approaches such as thermal DFT or PIMC within the fixed-node approximation. They also serve as direct predictions for upcoming XRTS experiments with hydrogen jets and ICF plas
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[slides and audio] Ab initio density response and local field factor of warm dense hydrogen