Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems

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 ${\mathrm{J}}_1-{\mathrm{J}}_2$ Heisenberg models, both in 1 and 2 dimensions. Our results indicate that spin AGP is a promising starting point for modeling spin systems.

16 pages, 14 figures

References in corpus (18)

• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Implementation of Spin Hamiltonians in Optical Lattices
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Probing many-body dynamics in a two dimensional dipolar spin ensemble
• Systematic electronic structure in the cuprate parent state from quantum many-body simulations
• Geminal replacement models based on AGP
• Exploring non-linear correlators on AGP
• Deformed Symmetry Structures and Quantum Many-body Scar Subspaces
• Lie Algebraic Similarity Transformed Hamiltonians for Lattice Model Systems
• Construction of linearly independent non-orthogonal AGP states
• AGP-based unitary coupled cluster theory for quantum computers
• Motif magnetism and quantum many-body scars
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems
• Colorful points in the XY regime of XXZ quantum magnets
• State preparation of AGP on a quantum computer without number projection

Cited by in corpus (5)

• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Symmetry-projected cluster mean-field theory applied to spin systems
• Correlated pair ansatz with a binary tree structure
• Linear combinations of cluster mean-field states applied to spin systems
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems