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Register a new userAb initio thermodynamic results for the degenerate electron gas at finite temperature
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The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids and much more. Accurate thermodynamic data for the UEG are an essential ingredient for many-body theories, in particular, density functional theory. Recently, first-principle restricted path integral Monte Carlo results became available which, however, due to the fermion sign problem, had to be restricted to moderate degeneracy, i.e. low to moderate densities with $r_s={bar r}/a_B gtrsim 1$. Here we present novel first-principle configuration PIMC results for electrons for $r_s leq 1$. We also present quantum statistical data within the $e^4$-approximation that are in good agreement with the simulations at small to moderate $r_s$.
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In a classical plasma the momentum distribution, $n(k)$, decays exponentially, for large $k$, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, $n_infty(k)sim k^{-8}$ has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive textit{ab initio} results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the $k^{-8}$ asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e. the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.
We present extensive new textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and temperatures. This allows us to study the nontrivial exchange--correlation induced increase of low-momentum states around the Fermi temperature, and to investigate its connection to the related lowering of the kinetic energy compared to the ideal Fermi gas. In addition, we investigate the impact of quantum statistics on both $n(mathbf{k})$ and the off-diagonal density matrix in coordinate space, and find that it cannot be neglected even in the strongly coupled electron liquid regime. Our results were derived without any nodal constraints, and thus constitute a benchmark for other methods and approximations.
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the epxerimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high density plasmas are needed which crucially depend on the quality of the thermodynamic properties of the quantum degenerate correlated electrons. Recent fixed node path integral Monte Carlo (RPIMC) data are the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter $r_s$ becomes smaller than $1$. Here we present new improved direct fermionic PIMC simulations that are exptected to be more accurate than RPIMC at high densities.
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Greens functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Greens function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.
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 $S(mathbf{q},omega)$ constitutes a key quantity as it is directly measured in X-ray Thomson (XRTS) scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first textit{ab initio} results for $S(mathbf{q},omega)$ 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 $G(mathbf{q},omega)$. In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for $S(mathbf{q},omega)$ over substantial parts of the warm dense matter regime.
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