Effective spin theories for edge magnetism in graphene zigzag ribbons

TL;DR

This paper systematically investigates the validity of simplified effective models for edge magnetism in graphene zigzag ribbons, demonstrating their robustness and enabling studies of complex correlation effects beyond traditional computational methods.

Contribution

It provides a thorough analysis of the reduction of bulk effects to edge models, validating their use in diverse geometries and facilitating advanced correlation physics studies.

Findings

Reduction to edge state models is justified in general geometries.

Effective models enable non-mean-field correlation physics studies.

Framework allows system size scaling beyond conventional methods.

Abstract

We report a thorough study of the reducibility of edge correlation effects in graphene to much-simplified effective models for the edge states. The latter have been used before in specially tailored geometries. By a systematic investigation of corrections due to the bulk states in second order perturbation theory, we show that the reduction to pure edge state models is well-justified in general geometries. The framework of reduced models discussed here enables the study of non-mean-field correlation physics for system sizes far beyond the reach of conventional methods, such as, e.g., quantum Monte-Carlo.