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Functional renormalization group for fermions in three dimensions

三维费米子的功能重整化群

基本信息

批准号：
289598096
负责人：
Professor Dr. Carsten Honerkamp
金额：
--
依托单位：
Institut für Theoretische Festkörperphysik C
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2021-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/289598096?language=en
关键词：
Functional renormalization group fermions three

项目摘要

The goal of this theory project is to devise and apply a functional renormalization group (fRG) scheme for interacting electrons in three-dimensional (3D) lattices. Over the last two decades, fRG has been used to explore interaction effects in a multitude of zero-, one- and two-dimensional model systems, but 3D systems were essentially out of range because of numerical limitations. Particular advantages of the fRG are its unbiasedness as to what the dominant interaction tendencies at low scales are, and that the functional nature of the flow equations allows one to obtain a rather detailed picture of the effective low-energy physics, e.g. for the effective interactions. These strengths would of course also be helpful in the analysis of 3D interacting electron systems. Recent advances in the fRG, most importantly a technique called vertex decomposition, have made the description of the effective interaction much more efficient, both regarding numerical aspects as well as for the physical understanding of its structure. Hence, new extensions can be addressed. Here, we plan to develop vertex decomposition techniques for general three-dimensional interacting electron systems and to apply them to important model cases. As a first application of the 3D fRG approach, we envisage the study of linear and quadratic band crossing point models that have recently been considered as hosting non-Fermi liquid behavior, unconventional charge screening and interaction-induced topological states.

该理论项目的目标是设计并应用函数重正化群 (fRG) 方案来实现三维 (3D) 晶格中电子的相互作用。在过去的二十年中，fRG 已被用来探索多种零维、一维和二维模型系统中的相互作用效应，但由于数值限制，3D 系统基本上超出了范围。 fRG 的特殊优点是它对低尺度下的主要相互作用趋势没有偏见，并且流动方程的函数性质允许人们获得有效低能物理的相当详细的图像，例如以实现有效的互动。这些优势当然也有助于分析 3D 相互作用电子系统。 fRG 的最新进展，最重要的是一种称为顶点分解的技术，使得有效相互作用的描述更加有效，无论是在数值方面还是在对其结构的物理理解方面。因此，可以解决新的扩展问题。在这里，我们计划开发通用三维相互作用电子系统的顶点分解技术，并将其应用于重要的模型案例。作为 3D fRG 方法的首次应用，我们设想研究线性和二次能带交叉点模型，这些模型最近被认为具有非费米液体行为、非常规电荷筛选和相互作用引起的拓扑状态。