Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems

TL;DR

This paper introduces a spin-adapted antisymmetrized geminal power (AGP) approach for modeling strongly correlated spin systems, demonstrating its effectiveness through benchmarks on well-known quantum spin models.

Contribution

It extends the AGP framework to spin systems using a spin su(2) algebra, implementing and benchmarking spin AGP and related correlation methods.

Findings

Spin AGP effectively models 1D and 2D spin systems.

Benchmark results show promising accuracy of spin AGP.

Spin AGP provides a new reference for strongly correlated spin models.

Abstract

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.