Many-body delocalization dynamics in long Aubry-Andr\'e quasiperiodic chains

We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-Andr\'e model of many-body localization. Using the time-dependent variational principle, we assess the late-time behaviour for chains up to $L = 50$. We find that the choice of periodicity $\Phi$ of the quasi-periodic field influences the dynamics. Finite-size effects on the critical disorder $W_c$ are much weaker than in the purely random case. For $\Phi = (\sqrt{5}-1)/2$ and interaction $\Delta = 1$, the model most frequently considered in the literature, we obtain $W_c = 4.8 \pm 0.2$ in units where the non-interacting transition is at $W = 2$. The data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.