Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)

TL;DR

This paper demonstrates that a variational PEPS approach with internal dimension D=2 effectively models the complex phases and magnetization phenomena in the frustrated Shastry-Sutherland antiferromagnet, bridging theory and experiment.

Contribution

It introduces a D=2 PEPS variational algorithm that captures both valence-bond crystal and Neel order in the Shastry-Sutherland model, advancing tensor network methods for frustrated systems.

Findings

Successfully models valence-bond crystal and Neel phases

Reproduces magnetization plateaus observed experimentally

Shows D=2 PEPS captures essential physics of frustrated magnets

Abstract

We have applied a variational algorithm based on Projected Entangled Pair States (PEPS) to a two dimensional frustrated spin system, the spin-1/2 antiferromagnetic Heisenberg model on the Shastry-Sutherland lattice. We use the class of PEPS with internal tensor dimension D=2, the first step beyond product states (D=1 PEPS). We have found that the D=2 variational PEPS algorithm is able to capture the physics in both the valence-bond crystal and the Neel ordered state. Also the spin-textures giving rise to the magnetization plateaus seen in experiments on SrCu$_2$(BO$_3$)$_2$ are well reproduced. This shows that PEPS with the smallest nontrivial internal dimension, D=2, can provide valuable insights into frustrated spin-systems.