A Conjecture on Antisymmetrized Geminal Power Wavefunctions

TL;DR

This paper conjectures that antisymmetrized geminal power wavefunctions can be expressed as products of orthogonal geminals, challenging their traditional physical interpretation, supported by proofs in simple cases and numerical evidence in complex ones.

Contribution

It introduces a conjecture linking AGP wavefunctions to orthogonal geminal products and provides proofs and numerical evidence supporting this claim.

Findings

Conjecture holds in simple cases

Numerical evidence supports conjecture in complex cases

Questions the physical interpretation of AGP wavefunctions

Abstract

We conjecture that ``Antisymmetrized Geminal Power'' wave functions, and, in particular, those of extreme type in Coleman's terminology (i.e. with all geminal coefficients equal), can always be rewritten as antisymmetrized products of geminals orthogonal to each other. We prove this conjecture in simple cases and provide numerical evidence that it holds true in more complicated examples. Establishing the validity of this conjecture is important as it questions the physical interpretation of AGP wavefunctions.