An efficient localized basis set for quantum Monte Carlo calculations on condensed matter

TL;DR

This paper introduces a localized basis set based on B-splines for quantum Monte Carlo calculations, enabling faster computations while maintaining accuracy, and seamlessly integrating with standard DFT codes.

Contribution

The authors develop and validate an efficient, unbiased, and systematically improvable localized basis set using B-splines for QMC, compatible with existing DFT workflows.

Findings

Speed-up of 10 to 100 times over plane-waves

Accurate results for silicon and magnesium oxide systems

Seamless interface between DFT and QMC calculations

Abstract

We present an efficient scheme for representing many-body wavefunctions in quantum Monte Carlo (QMC) calculations. The scheme is based on B-splines (blip functions), which consist of localized cubic splines centred on the points of a regular grid. We show that blip functions are unbiased, systematically improvable, and conveniently obtained from any standard plane-waves density functional theory (PW-DFT) code, and therefore provide a convenient and natural interface between PW-DFT and QMC calculations. We present tests on a 16-atom system of Si in the $\beta$-tin structure, and on 2- and 8- atoms systems of MgO in the NaCl structure. We show that already with such small systems the speed-up of blip functions with respect to plane-waves is between one and two order of magnitudes, without compromising the accuracy.