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arXiv · 2408.11024

Multifractal statistics of non-Hermitian skin effect on the Cayley tree

Shu Hamanaka·Askar A. Iliasov·Titus Neupert·Tomáš Bzdušek·Tsuneya Yoshida
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Abstract

Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree by deriving the analytical expression of multifractal dimensions. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder.

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Shu Hamanaka, Askar A. Iliasov, Titus Neupert, Tomáš Bzdušek, Tsuneya Yoshida. 2024-08-20. Multifractal statistics of non-Hermitian skin effect on the Cayley tree. https://doi.org/10.1103/physrevb.111.075162

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