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Auxiliary field quantum Monte Carlo at the basis set limit: Application to lattice constants

Moritz Humer1,*, Martin Schlipf2, Zoran Sukurma3, Sajad Bazrafshan1, and Georg Kresse2,4

  • 1Computational Materials Physics & Vienna Doctoral School in Physics, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
  • 2VASP Software GmbH, Berggasse 21/14, A-1090 Vienna, Austria
  • 3Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/E136, A-1040 Vienna, Austria
  • 4Computational Materials Physics, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria

  • *Contact author: moritz.humer@univie.ac.at
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Phys. Rev. B 113, 235146 – Published 24 June, 2026

DOI: https://doi.org/10.1103/ynv2-vw97

Abstract

We present a plane-wave (PW) implementation of the auxiliary-field quantum Monte Carlo (AFQMC) method within the projector augmented-wave (PAW) formalism in the Vienna ab initio Simulation Package (VASP). By employing an exact inversion of the PAW overlap operator, our approach maintains cubic scaling while naturally incorporating all excitations defined by the PW cutoff. We benchmark this framework by calculating the equilibrium lattice constants and bulk moduli of C, BN, BP, and Si. Our analysis demonstrates that AFQMC systematically corrects the lack of long-range screening in MP2 and the missing higher-order exchange in RPA. We identify RPA as the optimal reference method because of the rapid convergence of the remaining short-range correlations with respect to supercell size. The resulting lattice constants exhibit a mean absolute relative error of 0.14% relative to experiment, establishing the method as a rigorous benchmark tool for structural properties of prototypical semiconductors and insulators.

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Phys. Rev. B 113, 235146– Published 24 June, 2026
  • Received 18 February 2026
  • Revised 22 April 2026
  • Accepted 8 June 2026
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