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

TL;DR

This paper introduces a new method to effectively eliminate finite-size effects in quantum Monte Carlo simulations of the uniform electron gas, enabling accurate thermodynamic limit predictions with minimal system size.

Contribution

The authors present a density response-based scheme to correct finite-size effects in static structure factors and interaction energies, achieving high accuracy with very small electron numbers.

Findings

Achieves ~0.2% accuracy in the thermodynamic limit for small systems

Effective across various densities and temperatures

Reduces computational cost for accurate simulations

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 $\sim0.2\%$ 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 $T$.