Atomic cluster expansion and wave function representations

TL;DR

This paper extends the atomic cluster expansion (ACE) framework to anti-symmetric functions, unifying linear wave function representations and suggesting new nonlinear parameterizations for quantum systems.

Contribution

It generalizes ACE to anti-symmetric functions and explores its application to wave function representations, offering a broad design space for future methods.

Findings

ACE can represent well-known wave functions linearly.

Nonlinear wave function parameterizations can be enhanced using ACE.

The paper proposes a new framework for designing wave function representations.

Abstract

The atomic cluster expansion (ACE) has been highly successful for the parameterisation of symmetric (invariant or equivariant) properties of many-particle systems. Here, we generalize its derivation to anti-symmetric functions. We show how numerous well-known linear representations of wave functions naturally arise within this framework and we explore how recent successful nonlinear parameterisations can be further enhanced by employing ACE methodology. From this analysis we propose a wide design space of promising wave function representations.