分层石墨烯模型
The Hierarchical Graphene model
摘要：
分层石墨烯模型是一个简单的玩具模型，它有助于理解超重正化系统中的重整化群流的机制。它基于石墨烯中相互作用电子的模型，朱利安尼和马斯特罗彼得罗对该模型进行了重整化群分析。分层石墨烯模型的分析比石墨烯简单得多，但人们不应该期望它能产生关于真实世界石墨烯的良好定量结果。相反，层次模型是有用的教学工具，以了解重整化群技术的核心概念。在本文中，我们将首先介绍一个模型的电子在石墨烯和建立一个重整化群处理，通过引入其格拉斯曼表示和尺度分解。然后我们定义了层次石墨烯模型并研究了它的重整化群流。从重整化群的角度来看，石墨烯非常简单：它是超重整化的。作为一个更复杂的系统的例子，我们重复了对Kondo模型的分析，这是一个强耦合的模型，具有非平凡的不动点。
英文摘要：
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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