Abstract

The recently introduced single-boson exchange (SBE) decomposition of the four-point vertex of interacting fermionic many-body systems is a conceptually and computationally appealing parametrization of the vertex. It relies on the notion of reducibility of vertex diagrams with respect to the bare interaction U, instead of a classification based on two-particle reducibility within the widely used parquet decomposition. Here, we re-derive the SBE decomposition in a generalized framework (suitable for extensions to, e.g., inhomogeneous systems or real-frequency treatments) following from the parquet equations. We then derive multiloop functional renormalization group (mfRG) flow equations for the ingredients of this SBE decomposition, both in the parquet approximation, where the fully two-particle irreducible vertex is treated as an input, and in the more restrictive SBE approximation, where this role is taken by the fully U-irreducible vertex. Moreover, we give mfRG flow equations for the popular parametrization of the vertex in terms of asymptotic classes of the two-particle reducible vertices. Since the parquet and SBE decompositions are closely related, their mfRG flow equations are very similar in structure.

Graphic abstract

中文翻译：

---

单玻色子交换 fRG 的多回路流​​动方程

摘要

最近引入的相互作用的费米子多体系统的四点顶点的单玻色子交换 (SBE) 分解是顶点的概念和计算上吸引人的参数化。它依赖于顶点图关于裸交互U的可还原性的概念，而不是基于广泛使用的镶木地板分解中的两粒子可还原性的分类。在这里，我们根据 parquet 方程在广义框架中重新推导 SBE 分解（适用于扩展，例如，非均匀系统或实频处理）。然后，我们推导出该 SBE 分解成分的多环泛函重整化群 (mfRG) 流动方程，包括在 parquet 近似中，其中完全双粒子不可约顶点被视为输入，以及在更具限制性的 SBE 近似中，其中这角色由完全U- 不可约顶点。此外，我们根据两粒子可约顶点的渐近类别给出了顶点的流行参数化的 mfRG 流动方程。由于 parquet 和 SBE 分解密切相关，因此它们的 mfRG 流动方程在结构上非常相似。

图形摘要