Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition

TL;DR

This paper introduces a tensor decomposition-based algorithm that significantly reduces the computational cost and memory requirements of auxiliary-field quantum Monte Carlo calculations in Gaussian bases, enabling more efficient electronic structure simulations.

Contribution

The paper presents a novel low-rank tensor decomposition method that lowers the scaling of AFQMC calculations from quartic to sub-quartic, improving efficiency for large systems.

Findings

Significant memory savings in AFQMC calculations.

Reduced computational time for larger systems.

Successful application to various molecular and material systems.

Abstract

We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as $\mathcal{O}(N^4)$ where $N$ is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and sub-quartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases we observe significant memory savings and, for larger systems, reduced, sub-quartic simulation time.