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.
@article{arxiv.1412.6938,
title = {Effective spin theories for edge magnetism in graphene zigzag ribbons},
author = {Cornelie Koop and Manuel J. Schmidt},
journal= {arXiv preprint arXiv:1412.6938},
year = {2015}
}