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arXiv · 2602.16679

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·Joonho Lee
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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 direct access to the thermodynamic and complete-basis-set limits. By combining tensor hypercontraction with $\mathbf{k}$-point symmetry, we reduce the computational and memory scaling of ab initio AFQMC for solids to $\mathcal O(N^3)$ and $\mathcal O(N^2)$, respectively, with an arbitrary basis, comparable to diffusion Monte Carlo. This enables direct and simultaneous thermodynamic-limit and complete-basis-set AFQMC calculations 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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Jinghong Zhang, Meng-Fu Chen, Adam Rettig, Tong Jiang, Paul J. Robinson, Hieu Q. Dinh, Anton Z. Ni, Joonho Lee. 2026-02-18. Ab Initio Auxiliary-Field Quantum Monte Carlo in the Thermodynamic Limit. https://arxiv.org/abs/2602.16679

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