The Finite Size Error in Many-body Simulations with long-Ranged Interactions

TL;DR

This paper analyzes the finite size errors in many-body simulations of charged particles and proposes a correction method based on the random phase approximation, applicable to systems like electron gas and silicon.

Contribution

It introduces a correction scheme for finite size errors in many-body simulations using the RPA, enabling accurate energy calculations from a single simulation.

Findings

Finite size corrections improve energy estimates in simulations.

The correction method is validated on electron gas and silicon.

Results show significant reduction in finite size errors.

Abstract

We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.