Weakly first-order melting of the 1/3 plateau in the Shastry-Sutherland model

TL;DR

This study uses iPEPS to analyze the melting process of the 1/3 plateau in the Shastry-Sutherland model, revealing a weakly first-order transition at a temperature consistent with experimental observations.

Contribution

It demonstrates the application of iPEPS to identify the melting transition of the 1/3 plateau and maps the phase diagram for the model relevant to SrCu$_2$(BO$_3$)$_2$.

Findings

The 1/3 plateau melts via a weakly first-order transition.

The transition temperature is around 4.8K, matching experimental data.

Broken symmetries are restored at a single temperature.

Abstract

We investigate the thermal properties of the 1/3 plateau in the Shastry-Sutherland model with infinite projected entangled-pair states (iPEPS) by performing the imaginary time evolution of the infinite temperature density matrix. We show that both the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ broken symmetries of the ground states are restored at a unique temperature where the correlation length has a peak, and that the melting of the plateau occurs via a single weakly first-order transition. We focus on the experimentally relevant coupling constants deep into the 1/3 plateau phase at $h = 1$ and $J'/J = 0.63$, which was estimated to describe the SrCu$_2$(BO$_3$)$_2$ compound. By computing the free energy we are able to locate the transition temperature around $T_c \simeq 4.8$K well above the temperature $T=2$K, at which the 1/3 plateau was observed in experiments. The investigation is supplemented by adding a bias term to the Hamiltonian and studying the induced crossover. We further map the transition line in the field-temperature phase diagram.