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

TL;DR

This paper introduces a scalable ab initio AFQMC method for solids that achieves thermodynamic and basis-set limits efficiently, enabling accurate simulations across various solid types without approximations.

Contribution

It combines tensor hypercontraction and k-point symmetry to reduce AFQMC computational scaling to N^3 and N^2, allowing direct thermodynamic-limit calculations for solids.

Findings

Achieves O(N^3) and O(N^2) scaling for AFQMC in solids.

Enables direct thermodynamic-limit and complete-basis-set calculations.

Establishes AFQMC as a versatile alternative to DMC and coupled-cluster methods.

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.