论文标题
分层石墨烯模型
The Hierarchical Graphene model
论文作者
论文摘要
分层石墨烯模型是一个简单的玩具模型，可用于了解超级符号系统中重新归一化组流的机制。它基于石墨烯中相互作用的电子模型，该模型由Giuliani和Mastropietro进行了重新归一化组分析。分层石墨烯模型的分析比石墨烯要简单得多，但是人们不应该期望它会产生有关现实世界石墨烯的良好定量结果。相反，层次模型是一种教学工具，可以理解重新归一化组技术的核心概念。在本文中，我们将首先引入石墨烯中电子模型，并通过引入其Grassmann的代表和尺度分解来设置重新归一化组的治疗。然后，我们定义分层石墨烯模型，并研究其重新归一化组流量。从重新归一化组的角度来看，石墨烯非常简单：它是超级符号的。作为一个更复杂的系统的说明，我们重复了Kondo模型的分析，该模型是具有非平凡固定点的强耦合模型。
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.
