Hofstadter's Butterfly in AdS$_3$ Black Holes

• URL: http://arxiv.org/abs/2604.14335v1
• Date: Wed, 15 Apr 2026 18:40:36 GMT
• Title: Hofstadter's Butterfly in AdS$_3$ Black Holes
• Abstract summary: We derive the reduced Dirac Hamiltonian on the non-rotating BTZ background and use its redshift structure to construct a gauge-covariant single-band lattice model on the constant-time BTZ cylinder.<n>We show that weaker curvature sharpens the butterfly-like fragmentation, whereas larger horizons suppress both magnetic and Aharonov--Bohm response by creating weakly dispersing near-horizon states.
• Score: 1.5899159309486681
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive the reduced Dirac Hamiltonian on the non-rotating BTZ background and use its redshift structure to construct a gauge-covariant single-band lattice model on the constant-time BTZ cylinder. In equal-area coordinates the AdS radius $L$ fixes the local Gaussian curvature, while the horizon radius $r_h$ fixes the throat size and the strength of the near-horizon redshift. The lattice model therefore has a direct geometric interpretation and is not presented as an unshown reduction of the two-component Dirac lattice. Its angular Fourier transform yields an exact curved Harper equation with BTZ-dependent hopping amplitudes and a consistent dimensionless angular quasi-momentum. We then supplement global parameter scans with state-resolved diagnostics: spectra color-coded by mean radius, local density of states, direct flux-response versus radius correlations, and Aharonov--Bohm spectral flow and persistent current on the BTZ cycle. These results show that weaker curvature sharpens the butterfly-like fragmentation, whereas larger horizons suppress both magnetic and Aharonov--Bohm response by creating weakly dispersing near-horizon states.

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