## A beginner's guide to non-abelian iPEPS for correlated fermions

Benedikt Bruognolo, Jheng-Wei Li, Jan von Delft, Andreas Weichselbaum

SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021

- doi: 10.21468/SciPostPhysLectNotes.25
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### Abstract

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.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Benedikt Bruognolo, -
^{1}^{2}Jheng-Wei Li, -
^{1}^{2}Jan von Delft, -
^{1}^{2}^{3}Andreas Weichselbaum

^{1}Ludwig-Maximilians-Universität München / Ludwig Maximilian University of Munich [LMU]^{2}Munich Center for Quantum Science and Technology [MCQST]^{3}Brookhaven National Laboratory [BNL]