相关费米子的非阿贝尔iPEPS的初学者指南
A beginner's guide to non-abelian iPEPS for correlated fermions
摘要：
无限投射纠缠对态（iPEPS）是研究相互作用的二维费米子系统的有力工具。在这篇综述中，我们讨论了这种张量网络（TN）模拟器的iPEPS结构和一些基本性质。特别关注的是（i）一个温和的介绍图形TN表示形成的基础上推导出复杂的数值算法，及（ii）充分利用非阿贝尔对称性的多带晶格模型的费米iPEPS治疗的技术进步。利用非阿贝尔对称性大大提高了算法的性能，使治疗的费米子系统的键尺寸$D=24$上的正方形晶格。各种复杂的二维（2D）模型，从而成为数字访问。在这里，我们提出了第一个有希望的结果，两种类型的多带哈伯德模型，一个与$2$带的自旋费米子的$\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$对称性，其他与$3$口味的无自旋费米子的$\mathrm{SU}(3)_\mathrm{flavor}$对称性。
英文摘要：
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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