Identifying topological order in the Shastry-Sutherland model via entanglement entropy

TL;DR

This paper investigates the topological order in the Shastry-Sutherland model by calculating entanglement entropy, providing evidence for a topologically ordered phase in a highly frustrated quantum antiferromagnet.

Contribution

It demonstrates the presence of a topologically ordered state in the Shastry-Sutherland model using entanglement entropy analysis with the Kitaev-Preskill method.

Findings

Identification of a finite topological entanglement entropy in the model

Evidence for an exotic topologically ordered phase

Clarification of the nature of the intermediate phase

Abstract

It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, $-\gamma$, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction [A. Kitaev and J. Preskill, Phys. Rev. Lett. {\bf 96}, 110404 (2006)] we extract a finite topological term, $-\gamma$, in the region of bond-strength parameter space corresponding to high geometrical frustration. Thus, we provide strong evidence for the existence of an exotic topologically ordered state and shed light on the nature of this model's strongly frustrated, and long controversial, intermediate phase.