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arXiv:2610.25557

Signatures of slow particle transport in the interacting Aubry-André chain

S. Sharifan, M. Kiefer-Emmanouilidis, J. Sirker

Published Oct 18, 2026• 0 citations
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Abstract

Slow delocalization in strongly disordered many-body quantum chains can originate from two distinct mechanisms: rare resonances and avalanches, rooted in the energy statistics, or an energy-independent combinatorial path-entropy obstruction in operator space. Quasiperiodic potentials eliminate rare regions with similar potentials that are thought to be responsible for avalanche instabilities and modify the statistics of resonances, thus allowing us to delineate the two mechanisms. To do so, we numerically study the entanglement entropy $S(t)$, number entropy $S_N(t)$, and Hartley number entropy $S_H(t)$ following a quantum quench in the interacting Aubry-André chain with disorder strength $D$. We find $S(t)\simμ\ln t$, $S_N(t)\simν\ln\ln t$ with growth rates $μ\simν\sim D^{-γ}$ and $γ\approx 3$, the same behavior that was previously found in the case of quenched disorder. Furthermore, the saturation values $S_H(t\to\infty)$ continue to grow with system size $L$ as $\ln L$, a growth that persists for $D\gtrsim 8$ where MBL was argued to be stable. The similarity of the quasi-periodic and quenched disorder cases points to a common origin of the slow particle transport that does not rely on rare-region avalanches and persists despite strongly modified resonance statistics.

DOI
10.48550/arxiv.2610.25557

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The single-particle eigenstates of the Aubry-Andr\'e-Harper model are known to show a delocalization-localization transition at a finite strength of the quasiperiodic disorder. In this work, we point out that an intimate relationship exists between the subband structure of the spectrum and transport properties of the model. To capture the transport properties, we have not only used a variety of single-particle measures like inverse participation ratio, and von Neumann entropy, but also many-particle measures such as persistent current and its variance, and many-body entanglement entropy. The many-particle measures are very sensitive to the subband structure of the spectrum. Even in the delocalized phase, surprisingly the entanglement entropy is substantially suppressed when the Fermi level is in the band gaps, whereas the persistent current is vanishingly small for the same locations of the Fermi level. The entanglement entropy seems to follow area law exclusively for these special locations of Fermi level or filling fractions of free fermions. A study of the standard deviation of persistent current offers further distinguishing features for the special fillings. In the delocalized phase, the standard deviation vs mean persistent current curves are discontinuous for the nonspecial values of filling fractions and continuous (closed) for the special values of filling fractions, whereas in the localized phase, these curves become straight lines for both types of filling fractions. We have also discussed how the results depend on the system size. Our results, especially on the persistent current, can potentially be tested experimentally using the present day setups based on ultracold atoms.