A Multilevel Method for Many-Electron Schr\"{o}dinger Equations Based on the Atomic Cluster Expansion

TL;DR

This paper extends the atomic cluster expansion framework to many-electron wave functions, developing a variational Monte Carlo method that leverages ACE's hierarchical structure for efficient quantum system modeling.

Contribution

It introduces a novel multilevel approach for many-electron Schrödinger equations using ACE, enabling efficient computation through a customized Monte Carlo algorithm.

Findings

Feasibility demonstrated on 1D systems

Efficient exploitation of ACE sparsity and hierarchy

Potential for scalable many-electron quantum simulations

Abstract

The atomic cluster expansion (ACE) (Drautz, 2019) yields a highly efficient and intepretable parameterisation of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we extend the practical applicability of the ACE framework to the computation of many-electron wave functions. To that end, we develop a customized variational Monte-Carlo algorithm that exploits the sparsity and hierarchical properties of ACE wave functions. We demonstrate the feasibility on a range of proof-of-concept applications to one-dimensional systems.