Anomalous response, re-emerging localization-transition and robust corner sates in self-similar peano fractal

Abstract

Anomalous spectral response from the non-interacting electrons on a peano fractal is recorded within tight-binding framework. It is observed that a minimal off-diagonal anisotropy can modulate the transport characteristics of the lattice. Drastic modification in the nature of the eigenstates has been validated through the workout of level spacing statistics. Further, a two-dimensional quasiperiodic Aubry-André and Harper variation in the overlap integral can invite re-entrant localization-delocalization transition for the self-similar model. This is associated with the possible existence of single-particle mobility edge in the energy landscape. Our results are corroborated by the evaluation of inverse participation ratio, fractal dimension and quantum dynamical response. The spectrum is shown to formulate a quantum butterfly pattern with the frequency of the modulation. Chiral symmetry protected edge states are found to be insensitive with respect to moderate diagonal disorder.

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BibTeX RIS

BibTeX

@misc{acharjee2026anomalous,
  title = {{Anomalous response, re-emerging localization-transition and robust corner sates in self-similar peano fractal}},
  author = {Rhiddha Acharjee and Sayan Bhattacharya and Atanu Nandy and Debnarayan Jana},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01099},
  eprint = {2611.01099},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01099},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Anomalous response, re-emerging localization-transition and robust corner sates in self-similar peano fractal
AU  - Rhiddha Acharjee
AU  - Sayan Bhattacharya
AU  - Atanu Nandy
AU  - Debnarayan Jana
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01099
UR  - https://arxiv.org/abs/2611.01099
AB  - Anomalous spectral response from the non-interacting electrons on a peano fractal is recorded within tight-binding framework. It is observed that a minimal off-diagonal anisotropy can modulate the transport characteristics of the lattice. Drastic modification in the nature of the eigenstates has been validated through the workout of level spacing statistics. Further, a two-dimensional quasiperiodic Aubry-André and Harper variation in the overlap integral can invite re-entrant localization-delocalization transition for the self-similar model. This is associated with the possible existence of single-particle mobility edge in the energy landscape. Our results are corroborated by the evaluation of inverse participation ratio, fractal dimension and quantum dynamical response. The spectrum is shown to formulate a quantum butterfly pattern with the frequency of the modulation. Chiral symmetry protected edge states are found to be insensitive with respect to moderate diagonal disorder.
ER  -

Abstract

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