A beginner's guide to non-abelian iPEPS for correlated fermions
A beginner's guide to non-abelian iPEPS for correlated fermions
复制标题
DOI：
10.21468/scipostphyslectnotes.25
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Benedikt Bruognolo;Jheng-Wei Li;J. Delft;A. Weichselbaum
中科院分区：
文献类型：
--
作者：
Benedikt Bruognolo;Jheng-Wei Li;J. Delft;A. Weichselbaum
无限投影纠缠对态(IPEPS)已成为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，我们讨论了张量网络(TN)ansatz的iPEPS结构和一些基本性质。特别关注的是(I)简单地介绍形成复杂数值算法的基础的图解TN表示，以及(Ii)充分利用非阿贝尔对称性来处理多带晶格模型的费米子iPEPS的技术进展。非阿贝尔对称性的利用大大提高了算法的性能，使得能够在正方形晶格上处理高达键维$D=24$的费米子系统。因此，各种复杂的二维(2D)模型变得可以在数值上使用。在这里，我们给出了两类多带Hubbard模型的第一个有希望的结果，一个是$2$带的自旋费米子，具有$\mathm{SU}(2)_\mathm{自旋}\oTimes\mathm{SU}(2)_\mathm{球体}$对称性，另一个是$3$的无自旋费米子的$\mathm{SU}(3)_\mathm{风味}$对称性。
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.