Finite size errors in quantum many-body simulations of extended systems

TL;DR

This paper advances the theory of finite size errors in quantum many-body simulations, introducing a Model Periodic Coulomb interaction that reduces these errors across various calculations.

Contribution

It extends the Model Periodic Coulomb interaction to all Coulomb interactions, improving accuracy in quantum many-body simulations of extended systems.

Findings

Model Periodic Coulomb interaction reduces finite size errors

Finite size effects are similar in electron promotion and addition/subtraction energies

Techniques are demonstrated with Hartree-Fock and quantum Monte Carlo methods

Abstract

Further developments are introduced in the theory of finite size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced Model Periodic Coulomb interaction [A. J. Williamson et al., Phys. Rev. B 55, R4851 (1997)] can be applied consistently to all Coulomb interactions in the system. The Model Periodic Coulomb interaction greatly reduces the finite size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground and excited state calculations. We demonstrate that the finite size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar.