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

• URL: http://arxiv.org/abs/2205.04174v2
• Date: Mon, 28 Nov 2022 16:59:38 GMT
• Title: Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Authors: A. M. Marques and R. G. Dias
• Abstract summary: Hermitian bipartite models are characterized by the presence of chiral symmetry and by Lieb's theorem. We introduce a class of non-Hermitian models with an arbitrary number of sublattices connected in a unidirectional and cyclical way.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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