Exact special twist method for quantum Monte Carlo simulations

TL;DR

The paper introduces the exact special twist (EST) method for quantum Monte Carlo simulations, which accurately reduces finite-size effects with lower computational cost by using a single wavefunction, improving efficiency in large periodic systems.

Contribution

The authors develop and validate the EST method, providing a systematic way to find the optimal twist that reproduces the infinite-size mean-field energy within an arbitrarily small error, outperforming traditional twist averaging.

Findings

EST effectively reduces finite-size errors in quantum Monte Carlo simulations.

EST achieves similar accuracy to twist averaging but with significantly lower computational cost.

EST performs well in calculating correlation functions like ionic forces and pair distribution functions.

Abstract

We present a systematic investigation of the special twist method introduced by Rajagopal $\textit{et al.}$ [ Phys. Rev. B 51, 10591 (1995) ] for reducing finite-size effects in correlated calculations of periodic extended systems with Coulomb interactions and Fermi statistics. We propose a procedure for finding special twist values which, at variance with previous applications of this method, reproduce the energy of the mean-field infinite-size limit solution within an adjustable (arbitrarily small) numerical error. This choice of the special twist is shown to be the most accurate single-twist solution for curing one-body finite-size effects in correlated calculations. For these reasons we dubbed our procedure "exact special twist" (EST). EST only needs a fully converged independent-particles or mean-field calculation within the primitive cell and a simple fit to find the special twist along a specific direction in the Brillouin zone. We first assess the performances of EST in a simple correlated model such as the 3D electron gas. Afterwards, we test its efficiency within $\textit{ab initio}$ quantum Monte Carlo simulations of metallic elements of increasing complexity. We show that EST displays an overall good performance in reducing finite-size errors comparable to the widely used twist average technique but at a much lower computational cost, since it involves the evaluation of just one wavefunction. We also demonstrate that the EST method shows similar performances in the calculation of correlation functions, such as the ionic forces for structural relaxation and the pair radial distribution function in liquid hydrogen. Our conclusions point to the usefulness of EST for correlated supercell calculations, our method will be particularly relevant when the physical problem under consideration requires large periodic cells.