Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids

TL;DR

This paper develops a theoretical framework for correcting finite size effects in zero-temperature Quantum Monte Carlo calculations of electronic liquids and solids, introducing new methods to improve accuracy and reduce biases.

Contribution

It presents a general theory for finite size extrapolations, introduces effective procedures for correction, and discusses treatment of backflow wavefunctions in electronic QMC simulations.

Findings

Finite size bias can be significantly reduced with small system sizes.

New methods improve the accuracy of energy calculations for hydrogen and helium systems.

Effective procedures simplify the correction of finite size effects.

Abstract

Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation functions. We introduce new effective procedures, such as using the potential and wavefunction split-up into long and short range functions to simplify the method and we discuss how to treat backflow wavefunctions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.