Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices

Abstract

Hermitian bipartite models are characterized by the presence of chiral symmetry and by Lieb's theorem, which derives the number of zero-energy flat bands of the model from the imbalance of sites between its two sublattices. Here, we introduce a class of non-Hermitian models with an arbitrary number of sublattices connected in a unidirectional and cyclical way and show that the number of zero-energy flat bands of these models can be found from a generalized version of Lieb's theorem, in what regards its application to noninteracting tight-binding models, involving the imbalance between each sublattice and the sublattice of lowest dimension. Furthermore, these models are also shown to obey a generalized chiral symmetry, of the type found in the context of certain clock or parafermionic systems. The main results are illustrated with a simple toy model, and possible realizations in different platforms of the models introduced here are discussed.

13 pages, 7 figures

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Cited by in corpus (5)

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• Topological $n$-root Su-Schrieffer-Heeger model in a non-Hermitian photonic ring system
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices
• Exceptional flat bands in bipartite non-Hermitian lattices