Energy dispersion relation of the antiferromagnetic Shastry-Sutherland lattice

Abstract

In this project, we investigate the ground state properties of correlated electrons on the Shastry-Sutherland (SS) lattice, a 2-dimensional geometrically frustrated lattice which has attracted great interest in recent times in the context of quantum magnets. We first study the simplest possible model - the tight-binding model, for initial analysis. Further interaction terms are then added, so that one obtains the Hubbard model. Finally, spin-orbit coupling (between electrons and sites) terms are included, thus destroying spin-degeneracy. This is known as the Kane-Mele Hubbard model, which is expected to provide a rich variety of topological phases on the SS lattice. An important way to shed light on a system's electronic properties is to study its energy dispersion relation. This reveals various features, such as band structure, conductivity, and Hall conductance. The focus of this study would be to calculate the energy dispersion relations of each of the models mentioned. Some physical interpretations may be made about the physical observables, thus providing us with clues about its macroscopic behaviour. We start with a brief discussion of the mathematical framework used, and also an introduction to the respective models used; then, a brief discussion of the methodology and results is presented. The fi nal part of this report discusses the limitations of this study, and also provide suggestions on future endeavours or possible extensions of the project.