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

Journal Article · Thu Feb 25 00:00:00 EST 2021 · SciPost Physics Lecture Notes

DOI:https://doi.org/10.21468/SciPostPhysLectNotes.25· OSTI ID:1767343

Bruognolo, Benedikt ^[1]; Li, Jheng-Wei ^[1]; von Delft, Jan ^[1]; Weichselbaum, Andreas ^[2]

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1. Ludwig Maximilian University of Munich, Munich Center for Quantum Science and Technology
2. Ludwig Maximilian University of Munich, Munich Center for Quantum Science and Technology, Brookhaven National Laboratory

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 $D=24$ 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 $2$ bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb} $SU(2{)}_{spin}\otimes SU(2{)}_{orb}$ symmetry, the other with 3 $3$ flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor} $SU(3{)}_{flavor}$ symmetry.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0012704
• OSTI ID: 1767343
• Journal Information: SciPost Physics Lecture Notes, Journal Name: SciPost Physics Lecture Notes; ISSN 2590-1990
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English