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=24D=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
22
bands of spinful fermions of \mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}SU(2)spin⊗SU(2)orb
symmetry, the other with 33
flavors of spinless fermions of \mathrm{SU}(3)_\mathrm{flavor}SU(3)flavor
symmetry.
Stable iPEPO Tensor-Network Algorithm for Dynamics of Two-Dimensional Open Quantum Lattice Models
