The Hierarchical Graphene model
Ian Jauslin
2022
Abstract
The hierarchical graphene model is a simple toy model which is useful to understand the mechanics of renormalization group flows in super-renormalizable systems. It is based on a model of interacting electrons in graphene, for which the renormalization group analysis was carried out by Giuliani and Mastropietro. The analysis of the hierarchical graphene model is significantly simpler than graphene, but one should not expect it to produce good quantitative results about real-world graphene. Rather, the hierarchical model is useful as a teaching tool to understand the core concepts of renormalization group techniques. In this paper, we will first introduce a model for electrons in graphene and set it up for a renormalization group treatment by introducing its Grassmann representation and scale decomposition. We then define the hierarchical graphene model and study it's renormalization group flow. From a renormalization group point of view, graphene is quite simple: it is super-renormalizable. As an illustration of a more complicated system, we repeat the analysis for the Kondo model, which is a strongly coupled model with a non-trivial fixed point.
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LaTeX source:
- tarball: 22jb-1.1.tar.gz
- git repository: 22jb-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
Computation
The computation of the beta functions for the hierarchical graphene and hierarchical s-d model were carried out using meankondo v 1.5. The meankondo configuration files for these models are available from the meankondo page: http://ian.jauslin.org/software/meankondo, under the heading "meankondo_projects".Other releases
- arXiv preprint: arXiv:2206.08239.
Related articles
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[BGJ15]: Kondo effect in a fermionic hierarchical model
Giuseppe Benfatto, Giovanni Gallavotti, Ian Jauslin, 2015
(published in Journal of Statistical Physics, volume 161, issue 5, pages 1203-1230, 2015)
pdf, source -
[GJ15]: Kondo effect in the hierarchical s-d model
Giovanni Gallavotti, Ian Jauslin, 2015
(This letter is an extension of [BGJ15] to the s-d model)
(published in Journal of Statistical Physics, volume 161, issue 5, pages 1231-1235, 2015)
pdf, source -
[GiJ15]: The ground state construction of bilayer graphene
Alessandro Giuliani, Ian Jauslin, 2015
(published in Reviews in Mathematical Physics, volume 28, issue 8, number 1650018, 2016)
pdf, source
Talks
This work has been presented at the following conferences: