Eigenstate transitions and critical transport in 3D Aubry-André model
Abstract
We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility χ and the eigenstate fractal dimension d(1) [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent z, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of z=3.
Related
- Localization Transitions in a Half-Filled Helical Aubry-André Model
- Signatures of slow particle transport in the interacting Aubry-André chain
- Fibonacci number systems and the localization criterion in the many-body Aubry-André model
- An Aubry-André localized optical lattice clock
- Statistical delocalization in the Anyonic Aubry-André model
BibTeX
@misc{das2026eigenstate,
title = {{Eigenstate transitions and critical transport in 3D Aubry-André model}},
author = {Pragna Das and Lev Vidmar and Miroslav Hopjan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15842},
eprint = {2610.15842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15842},
}
RIS
TY - UNPB
TI - Eigenstate transitions and critical transport in 3D Aubry-André model
AU - Pragna Das
AU - Lev Vidmar
AU - Miroslav Hopjan
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15842
UR - https://arxiv.org/abs/2610.15842
AB - We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility χ and the eigenstate fractal dimension d^(1) [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent z, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of z=3.
ER -