Overcoming finite-size effects in electronic structure simulations at extreme conditions

Abstract

\textit{Ab initio} quantum Monte Carlo (QMC) methods in principle allow for the calculation of exact properties of correlated many-electron systems, but are in general limited to the simulation of a finite number of electrons $N$ in periodic boundary conditions. Therefore, an accurate theory of finite-size effects is indispensable to bridge the gap to realistic applications in the thermodynamic limit. In this work, we revisit the uniform electron gas (UEG) at finite temperature as it is relevant to contemporary research e.g. in the field of warm dense matter. In particular, we present a new scheme to eliminate finite-size effects both in the static structure factor $S(q)$ and in the interaction energy $v$, which is based on the density response formalism. We demonstrate that this method often allows to obtain $v$ in the TDL within a relative accuracy of $\sim 0.2\%$ from as few as $N=4$ electrons without any empirical choices or knowledge of results for other values of $N$. Finally, we evaluate the applicability of our method upon increasing the density parameter $r_s$ and decreasing the temperature $T$.

arXiv admin note: text overlap with arXiv:2101.05498

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• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids
• Unravelling the nonlinear ideal density response of many-body systems
• Energy response and spatial alignment of the perturbed electron gas
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes