Numerical Jordan-Wigner approach for two dimensional spin systems

TL;DR

This paper introduces a numerical variational method based on Jordan-Wigner transformation to study two-dimensional spin systems, successfully applied to the antiferromagnetic XXZ model, showing convergence to known ground states.

Contribution

The paper develops a self-consistent variational approach using Jordan-Wigner transformation for 2D spin systems, demonstrating its effectiveness on the XXZ model.

Findings

Method converges to Néel ordered ground state for SU(2) case

Potential utility for frustrated or disordered systems

Applicable to various anisotropies in the XXZ model

Abstract

We present a numerical self consistent variational approach based on the Jordan-Wigner transformation for two dimensional spin systems. We apply it to the study of the well known quantum (S=1/2) antiferromagnetic XXZ system as a function of the easy-axis anisotropy \Delta on a periodic square lattice. For the SU(2) case the method converges to a N\'eel ordered ground state irrespectively of the input density profile used and in accordance with other studies. This shows the potential utility of the proposed method to investigate more complicated situations like frustrated or disordered systems.