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

• URL: http://arxiv.org/abs/2408.11024v2
• Date: Wed, 26 Feb 2025 17:23:22 GMT
• Title: Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Abstract summary: Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored.<n>We show that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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