Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model

TL;DR

This paper explores how topological band theory, specifically topological quantum chemistry, can be extended to analyze the strongly correlated Kitaev honeycomb model, revealing insights into its excitation spectrum and edge modes.

Contribution

It demonstrates a novel approach to applying topological band theory to strongly correlated systems like the Kitaev model by associating spin operators with orbitals.

Findings

Band structure analysis of the Kitaev model using TQC

Identification of low-energy topological edge modes

Extension of topological band theory to strongly correlated systems

Abstract

In the study of quantum spin liquids, the Kitaev model plays a pivotal role due to the fact that its ground state is exactly known as well as the fact that it may be realized in strongly frustrated materials such as ${\alpha}$-RuCl${}_3$. While topological insulators and superconductors can be investigated by means of topological band theory -- in particular the topological quantum chemistry (TQC) formalism -- the Kitaev model evades such a treatment, as it is not possible to set up a proper single-particle Green's function for it. We instead associate spin operators with ``orbitals'' that give rise to a band structure. It is thereby possible to analyze the corresponding excitation spectrum engendered by these localized excitations by means of TQC. Special attention is given to the low-energy topological edge mode spectrum. Our work sheds light on the question how the TQC formalism may be generalized to strongly correlated and topologically ordered systems like the Kitaev model.