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Ab Initio Auxiliary-Field Quantum Monte Carlo in the Thermodynamic Limit

Jinghong Zhang, Meng-Fu Chen, Adam Rettig, Tong Jiang, Paul J. Robinson, Hieu Q. Dinh, Anton Z. Ni, and Joonho Lee*

  • Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

  • *Contact author: joonholee@g.harvard.edu
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Phys. Rev. X 16, 031044 – Published 19 August, 2026

DOI: https://doi.org/10.1103/dtly-b2lp

Abstract

Ab initio auxiliary-field quantum Monte Carlo (AFQMC) is a systematically improvable many-body method, but its application to extended solids has been severely limited by unfavorable computational scaling and memory requirements that obstruct rigorous access to the thermodynamic and complete-basis-set limits. By combining tensor hypercontraction with k-point symmetry, we reduce the computational and memory scaling of ab initio AFQMC for solids to O(N3) and O(N2), respectively, with an arbitrary basis, comparable to diffusion Monte Carlo. This enables simultaneous, controlled extrapolation of full-system AFQMC calculations to the thermodynamic and complete-basis-set limits across insulating, metallic, and strongly correlated solids, without embedding, local approximations, empirical finite-size corrections, or composite schemes. Our results establish AFQMC as a general-purpose, systematically improvable alternative to diffusion Monte Carlo and coupled-cluster methods for predictive ab initio simulations of solids, enabling accurate energies and magnetic observables within a unified framework.

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Popular Summary

Accurately predicting the properties of solids requires accounting for interactions among many electrons. However, high-accuracy many-electron methods become prohibitively expensive for realistic system sizes and large orbital basis sets. We developed a more efficient formulation of auxiliary-field quantum Monte Carlo that substantially reduces both its computational and memory requirements. This advance allows full-system calculations to be systematically extrapolated to the bulk and complete-basis-set limits, without relying on embedding, local approximations, empirical finite-size corrections, or composite schemes. We demonstrate the method for semiconductors, simple metals, and strongly correlated transition-metal oxides, accurately predicting cohesive energies and magnetic properties within a unified framework. Our work establishes auxiliary-field quantum Monte Carlo as a practical and systematically improvable approach for predictive simulations of solids.

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Phys. Rev. X 16, 031044– Published 19 August, 2026
  • Received 23 February 2026
  • Revised 29 April 2026
  • Accepted 27 July 2026
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