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Localization transitions in a half-filled helical Aubry-André model

Taylan Yildiz and B. Tanatar*

Balázs Hetényi

  • Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary; MTA-BME Lendület “Momentum” Open Quantum Systems Research Group, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary; and Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, H-1525 Budapest, P. O. Box 49, Hungary

  • *Contact author: tanatar@fen.bilkent.edu.tr
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Phys. Rev. B 114, 094206 – Published 24 August, 2026

DOI: https://doi.org/10.1103/c5wk-3ym5

Abstract

We investigate localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-André model with a structured Nth-neighbor hopping term of strength JN. This additional channel connects successive windings of an effective helical chain, introducing both a hopping scale and a geometric length scale into the localization problem. Under periodic boundary conditions, we identify the localization transition using a geometric Binder cumulant U4 constructed from the polarization amplitudes of the occupied many-body Slater determinant. The finite-size critical potential is extracted from the zero crossing of U4. At fixed helical range N, increasing JN shifts the transition toward larger quasiperiodic potential strengths. In contrast, varying N produces a strongly nonmonotonic phase boundary with pronounced spikelike enhancements of the critical potential. Using Fibonacci system sizes together with a Zeckendorf-shift construction for the particle number, we show that the dominant spike structure survives the thermodynamic-limit extrapolation. The largest enhancements are associated with helical ranges for which the phase shift 2πβN approaches an in-phase or antiphase resonance condition. We supplement the polarization analysis with occupied-state IPR and NPR, energy-resolved IPR maps, and the single-particle Fermi gap. The Fermi gap begins to open at the same crossover onset at which U4 departs from its conducting-regime plateau, providing a complementary spectral signature of the same insulating transition. The participation ratios show that, in the half-filled sectors studied here, this transition is also accompanied by a gradual and energy-dependent localization of the single-particle eigenstates.

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Phys. Rev. B 114, 094206– Published 24 August, 2026
  • Received 17 May 2026
  • Revised 23 July 2026
  • Accepted 31 July 2026
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