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

TL;DR

This paper introduces non-abelian symmetric iPEPS tensor networks for simulating complex 2D fermionic systems, highlighting algorithmic improvements and demonstrating results on multi-band Hubbard models.

Contribution

It presents a comprehensive beginner's guide to non-abelian fermionic iPEPS, emphasizing symmetry exploitation for enhanced computational performance.

Findings

Enabled treatment of fermionic systems up to bond dimension D=24

Achieved numerical results for multi-band Hubbard models with complex symmetries

Demonstrated the effectiveness of non-abelian symmetry exploitation in tensor networks

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.