Computational scheme for the spin-1/2 square lattice Heisenberg antiferromagnet based on an octapartite description of the square lattice

TL;DR

This paper presents a new octapartite parametrization scheme for the Hilbert space of the spin-1/2 square lattice Heisenberg antiferromagnet, enabling efficient modeling of the ground state with high accuracy and potential for broader applications.

Contribution

A novel octapartite Hilbert space parametrization scheme that simplifies modeling the ground state of the 2D Heisenberg antiferromagnet with reduced computational cost.

Findings

Achieved ground-state energies within 1% of known lowest values.

Successfully modeled systems with up to 64 spins using exact diagonalization.

The method is non-iterative and preserves spatial symmetries, enabling future extensions.

Abstract

We introduce a novel parametrization scheme for the Hilbert space of a spin-1/2 Heisenberg antiferromagnet (AFM) based on an octapartite description of the square lattice. Our formulation provides an efficient yet systematic way to model the singlet ground-state wave function within a truncated basis. We demonstrate its effectiveness by using exact diagonalization to study systems with up to 64 spins. At significantly reduced computational cost, we obtain ground-state energies within less than 1% of the lowest values published. The non-iterative nature of this formulation and the fact that spatial symmetries remain unexploited lead to opportunities for extensions such as the incorporation into established iterative methods and the application to interacting models, for example in the study of the propagation of charged fermions in a 2D antiferromagnet.