From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model

TL;DR

This paper introduces a generalized model connecting the Shastry-Sutherland and J1-J2 Heisenberg models, revealing a tri-critical point where phase transition nature changes, supported by advanced numerical simulations.

Contribution

It proposes a unified model bridging two important quantum spin models and identifies a tri-critical point in the phase diagram through large-scale numerical methods.

Findings

The phase transition between PVBS and AFM in the Shastry-Sutherland model is weak first-order.

A tri-critical point exists where the transition changes from first-order to continuous.

The model offers a realistic framework for studying Shastry-Sutherland materials like SrCu2(BO3)2.

Abstract

We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the $J_1$-$J_2$ Heisenberg model. By employing large scale Density Matrix Renormalization Group and Fully Augmented Matrix Product State calculations, combined with careful finite-size scaling, we find the phase transition between the plaquette valence bond state (PVBS) and Neel anti-ferromagnetic (AFM) phase in the pure Shastry-Sutherland model is a weak first one. This result indicates the existence of an exotic tri-critical point in the PVBS to AFM transition line in the phase diagram, as the transition in the $J_1$-$J_2$ Heisenberg model was previously determined to be continuous. We determine the location of the tri-critical point in the phase diagram at which first-order transition turns to continuous. Our generalized Shastry-Sutherland model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of Shastry-Sutherland materials like SrCu$_2$(BO$_3$)$_2$.