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

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 $S(t)\sim \mu \ln t$, $S_N(t)\sim \nu \ln \ln t$ with growth rates $\mu \sim \nu \sim D^{-\gamma }$ and $\gamma \approx 3$, the same behavior that was previously found in the case of quenched disorder. Furthermore, the saturation values $S_H(t\to \mathrm{\infty })$ 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.