Localization Transitions in a Half-Filled Helical Aubry-André Model
Abstract
We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-André model with an additional Nth-neighbor hopping term of strength JN. This long-range tunneling couples successive windings of an effective helical chain and introduces a second control parameter beyond the quasiperiodic potential strength Δ. Working with noninteracting fermions (typically at half filling), we diagnose the delocalization-localization transition using extensions of the modern theory of polarization. Specifically, we compute the polarization amplitudes of the many-body Slater-determinant ground state and construct a geometric Binder cumulant from polarization amplitudes. The critical potential where the localization transition happens is extracted from the sign change (zero crossing) of the geometric Binder cumulant. We map critical potential as a function of JN and the helical range N, finding that stronger helical hopping generally stabilizes the extended phase (shifting critical potential upward), while the N-dependence can display pronounced commensurability-induced spikes. We further compare the geometric Binder cumulant with the Fermi gap, which remains near zero at small values of potential and opens in the same parameter regime where the geometric Binder cumulant departs from extended phase. Finally, to take a controlled thermodynamic limit along Fibonacci system sizes, we employ a Zeckendorf-shift construction that fixes the many-body sector consistently as system size goes to infinity.
Versions
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BibTeX
@misc{yildiz2026localization,
title = {{Localization Transitions in a Half-Filled Helical Aubry-André Model}},
author = {Taylan Yildiz and B. Tanatar and Balázs Hetényi},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.18064},
eprint = {2605.18064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18064},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Localization Transitions in a Half-Filled Helical Aubry-André Model
AU - Taylan Yildiz
AU - B. Tanatar
AU - Balázs Hetényi
PY - 2026
DA - 2026/05/18
PB - arXiv
DO - 10.48550/arxiv.2605.18064
UR - https://arxiv.org/abs/2605.18064
AB - We study localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-André model with an additional Nth-neighbor hopping term of strength J_N. This long-range tunneling couples successive windings of an effective helical chain and introduces a second control parameter beyond the quasiperiodic potential strength Δ. Working with noninteracting fermions (typically at half filling), we diagnose the delocalization-localization transition using extensions of the modern theory of polarization. Specifically, we compute the polarization amplitudes of the many-body Slater-determinant ground state and construct a geometric Binder cumulant from polarization amplitudes. The critical potential where the localization transition happens is extracted from the sign change (zero crossing) of the geometric Binder cumulant. We map critical potential as a function of J_N and the helical range N, finding that stronger helical hopping generally stabilizes the extended phase (shifting critical potential upward), while the N-dependence can display pronounced commensurability-induced spikes. We further compare the geometric Binder cumulant with the Fermi gap, which remains near zero at small values of potential and opens in the same parameter regime where the geometric Binder cumulant departs from extended phase. Finally, to take a controlled thermodynamic limit along Fibonacci system sizes, we employ a Zeckendorf-shift construction that fixes the many-body sector consistently as system size goes to infinity.
ER -