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Estimates of the dynamic structure factor for the finite temperature electron liquid via analytic continuation of path integral Monte Carlo data

Thomas Chuna1,2,*, Nicholas Barnfield3, Jan Vorberger2, Michael P. Friedlander4, Tim Hoheisel5, and Tobias Dornheim1,2

  • *Contact author: t.chuna@hzdr.de
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Phys. Rev. B 112, 125112 – Published 4 September, 2025

DOI: https://doi.org/10.1103/4d4b-kgtk

Abstract

Understanding the dynamic properties of uniform electron gas (UEG) is important for numerous applications ranging from semiconductor physics to exotic warm dense matter. In this work, we apply the maximum entropy method (MEM), as implemented by Thomas Chuna et al., J. Phys. A Math. Theor. 58, 335203 (2025), to ab initio path integral Monte Carlo (PIMC) results for the imaginary-time correlation function F(q,τ) to estimate the dynamic structure factor S(q,ω) over an unprecedented range of densities at the electronic Fermi temperature. To conduct the MEM, we propose to construct the Bayesian prior μ from the PIMC data. Constructing the static approximation leads to a drastic improvement in S(q,ω) estimate over using the simpler random phase approximation (RPA) as the Bayesian prior. We present results for the strongly coupled electron liquid regime with rs=50,⋯,200, which reveal a pronounced roton-type feature and an incipient double peak structure in S(q,ω) for intermediate wave numbers at rs=200. We also find that our dynamic structure factors satisfy known sum rules, even though these sum rules are not enforced explicitly. To verify our results, we show that our MEM estimates converge to the RPA limit at higher densities and weaker coupling rs=2 and 5. Further, we compare with two different existing results at intermediate density and coupling strength rs=10 and 20, and we find good agreement with more conservative estimates. Combining all of our results for rs=2,5,10,20,50,100,200, we present estimates of a dispersion relation that show a continuous deepening of its minimum value at higher coupling. An advantage of our setup is that it is not specific to the UEG, thereby opening up new avenues to study the dynamics of real warm dense matter systems based on cutting-edge PIMC simulations in future works.

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Phys. Rev. B 112, 125112– Published 4 September, 2025
  • Received 26 March 2025
  • Revised 14 July 2025
  • Accepted 12 August 2025
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