Effective models for strong electronic correlations at graphene edges

TL;DR

This paper introduces a method to derive simplified low-energy models for electronic interactions at graphene edges, enabling feasible analysis of magnetic properties in complex and disordered edge structures.

Contribution

The authors develop a general approach to obtain effective low-energy theories for graphene edges, reducing degrees of freedom and allowing accurate magnetic property predictions beyond mean-field approximations.

Findings

Effective theories match quantum Monte-Carlo results for correlation functions.

Reduced models enable analysis of large and disordered graphene edges.

Heisenberg spin model captures magnetic features efficiently.

Abstract

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.