Momentum-space finite-size corrections for Quantum-Monte-Carlo calculations

TL;DR

This paper introduces a hybrid method combining real-space and momentum-space approaches to accurately correct finite-size errors in Quantum-Monte-Carlo simulations of extended solids, improving convergence and applicability.

Contribution

A novel hybrid method that models the structure factor in momentum space using real-space data, unifying and enhancing existing finite-size correction techniques in QMC calculations.

Findings

Hybrid method exactly maps onto MPC via integration

Improves convergence where MPC fails, especially in surface-like systems

Simplifies correction by dealing with a single-valued function

Abstract

Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite- size errors. In the case of Quantum-Monte-Carlo simulations, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real-space and momentum-space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surface-like systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and, hence, better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.