Exploring spin antisymmetrized geminal power Ansätze for strongly correlated spin systems

The antisymmetrized geminal power (AGP), a wave function equivalent to number-projected Hartree-Fock-Bogoliubov (HFB), and number-projected Bardeen-Cooper-Schrieffer (BCS) when working in the paired (natural orbitals) basis, has proven to be an excellent reference for strong pairing interactions. Several correlation methods have also been applied on top of AGP. In this work, we show how AGP can also be applied to spin systems by simply basing its formulation on a spin $su(2)$ algebra. We here implement spin AGP and spin AGP-based correlation techniques and benchmark them on the XXZ and ${\mathrm{J}}₁\text{\ensuremath{-}}{\mathrm{J}}₂$ Heisenberg models, both in one and two dimensions. Our results indicate that spin AGP is a promising starting point for modeling spin systems.