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

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 $J^{\prime }/J=0.63$, 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.