For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of m-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.

中文翻译：

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自旋模型的伪费米子功能重整化群

几十年来，受挫的量子磁体一直是凝聚态物质科学进步和创新的种子。近年来，由于量子信息和量子计算的突破，低维量子磁性的数值工具得到了蓬勃发展和改进，高维量子磁性可以被认为是最后的前沿，其中强量子纠缠、多重有序通道和顺磁性的多种方式达到顶峰。与此同时，晶体合成方面的努力导致有形受挫磁体的数量显着增加，这些磁体本质上通常是三维的，迫切需要定量理论建模。我们回顾了赝费米子 (PF) 和赝马约拉纳 (PM) 功能重正化群 (FRG) 及其解决高维受挫量子磁性的特定能力。PFFRG 于十多年前首次开发，它根据 Abrikosov 伪费米子解释了海森堡模型哈密顿量，然后将其用图解恢复方案进行处理，该方案表示为重正化群流米-粒子赝费米子顶点。本文回顾了 PFFRG 和 PMFRG 的最新技术，并讨论了它们在受阻磁性示例领域的应用，但最重要的是，它使每个人都可以了解这些方法的算法和实现细节。通过降低其应用的准入门槛，我们希望这篇综述将有助于建立 PFFRG 和 PMFRG 作为解决更高空间维度中受挫量子磁性的数值方法。