  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
$\mathrm{J_1-J_2}$ Heisenberg models, both in 1 and 2 dimensions. Our results
indicate that spin AGP is a promising starting point for modeling spin systems.
