Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

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非阿贝尔相关费米子的iPEPS初学者指南

无限投影纠缠对态（iPEPS）已经成为研究相互作用的二维铁离子系统的有力工具。在这篇综述中，我们讨论了iPEPS的构造以及该张量网络（TN）ansatz的一些基本属性。特别关注（i）简要介绍TN图解表示法，这些图式是推导复杂数值算法的基础，以及（ii）充分利用非阿贝尔对称性进行多频带晶格模型的铁离子iPEPS处理的技术进步。利用非阿贝尔对称性可显着提高算法的性能，从而能够在方形晶格上处理高达键尺寸$ D = 24 $的铁离子系统。因此，各种复杂的二维（2D）模型都可以在数值上访问。这里，