Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model
Abstract
We propose a q-deformation in the single-particle kinetic energy and investigate how it modifies the localization in the one-dimensional Aubry-André (AA) model. We construct a Hermitian q-deformed kinetic operator as a nonlinear function of the lattice translation operator, preserving the uniform lattice and recovering the conventional AA Hamiltonian continuously in the undeformed limit q→1. The deformation generates an infinite set of correlated odd-range kinetic processes, controlled by a single parameter q, rather than phenomenologically involving long-range hopping. Under the dual transformation, this long-range hopping appears as higher harmonics of the dual quasiperiodic potential, providing a controlled route for breaking the exact self-duality of the AA model, with q as the control parameter, consequently modifying the localization structure for q≠1. In contrast to the conventional AA model, where all eigenstates localize simultaneously at λc=2, the deformed model exhibits a fraction of delocalized states even beyond λc =2. An intermediate regime also emerges in the q−λ plane where localized and extended eigenstates coexist across the spectrum. We also propose a possible experimental realization of the hierarchy produced in the q-deformed kinetic setting in a periodically driven AA model.
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BibTeX
@misc{goswami2026localization,
title = {{Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model}},
author = {Arpita Goswami},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36446},
eprint = {2609.36446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36446},
}
RIS
TY - UNPB
TI - Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model
AU - Arpita Goswami
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36446
UR - https://arxiv.org/abs/2609.36446
AB - We propose a q-deformation in the single-particle kinetic energy and investigate how it modifies the localization in the one-dimensional Aubry-André (AA) model. We construct a Hermitian q-deformed kinetic operator as a nonlinear function of the lattice translation operator, preserving the uniform lattice and recovering the conventional AA Hamiltonian continuously in the undeformed limit q→1. The deformation generates an infinite set of correlated odd-range kinetic processes, controlled by a single parameter q, rather than phenomenologically involving long-range hopping. Under the dual transformation, this long-range hopping appears as higher harmonics of the dual quasiperiodic potential, providing a controlled route for breaking the exact self-duality of the AA model, with q as the control parameter, consequently modifying the localization structure for q≠1. In contrast to the conventional AA model, where all eigenstates localize simultaneously at λ_c=2, the deformed model exhibits a fraction of delocalized states even beyond λ_c =2. An intermediate regime also emerges in the q−λ plane where localized and extended eigenstates coexist across the spectrum. We also propose a possible experimental realization of the hierarchy produced in the q-deformed kinetic setting in a periodically driven AA model.
ER -