Application of a spherically averaged pair potential in ab initio path integral Monte Carlo simulations of a warm dense electron gas

Spherically averaged periodic pair potentials offer the enticing promise to provide accurate results at a drastically reduced computational cost compared to the traditional Ewald sum. In this work, we employ the pair potential by Yakub and Ronchi [] in path integral Monte Carlo (PIMC) simulations of the warm dense uniform electron gas. Overall, we find very accurate results with respect to Ewald reference data for integrated properties such as the kinetic and potential energy, whereas wavenumber-resolved properties such as the static structure factor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>S</a:mi><a:mo>(</a:mo><a:mi mathvariant="bold">q</a:mi><a:mo>)</a:mo></a:mrow></a:math>, the static linear density response <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>χ</c:mi><c:mo>(</c:mo><c:mi mathvariant="bold">q</c:mi><c:mo>)</c:mo></c:mrow></c:math>, and the static quadratic density response <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msup><e:mi>χ</e:mi><e:mrow><e:mo>(</e:mo><e:mn>2</e:mn><e:mo>)</e:mo></e:mrow></e:msup><e:mrow><e:mo>(</e:mo><e:mi mathvariant="bold">q</e:mi><e:mo>,</e:mo><e:mn>0</e:mn><e:mo>)</e:mo></e:mrow></e:mrow></e:math> fluctuate for small <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>q</g:mi></g:math>. In addition, we perform an analytic continuation to compute the dynamic structure factor <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>S</h:mi><h:mo>(</h:mo><h:mi mathvariant="bold">q</h:mi><h:mo>,</h:mo><h:mi>ω</h:mi><h:mo>)</h:mo></h:mrow></h:math> from PIMC results of the imaginary-time density-density correlation function <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>F</j:mi><j:mo>(</j:mo><j:mi mathvariant="bold">q</j:mi><j:mo>,</j:mo><j:mi>τ</j:mi><j:mo>)</j:mo></j:mrow></j:math> for both pair potentials. Our results have important implications for future PIMC calculations, which can be sped up significantly using the Yakub and Ronchi potential for the estimation of equation-of-state properties or <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>q</l:mi></l:math>-resolved observables in the noncollective regime, whereas a full Ewald treatment is mandatory to accurately resolve physical effects manifesting for smaller <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>q</m:mi></m:math>, including the evaluation of compressibility sum rules, the interpretation of x-ray scattering experiments at small scattering angles, and the estimation of optical and transport properties.