Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Abstract

We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to $L=50$. We find that the choice of periodicity $\Phi$ of the quasi-periodic field influences the dynamics. For $\Phi =(\sqrt{5}-1)/2$ (the inverse golden ratio) and interaction $\Delta =1$, the model most frequently considered in the literature, we obtain the critical disorder $W_c=4.8\pm 0.5$ in units where the non-interacting transition is at $W=2$. At the same time, for periodicity $\Phi =\sqrt{2}/2$ we obtain a considerably higher critical value, $W_c=7.8\pm 0.5$. Finite-size effects on the critical disorder $W_c$ are much weaker than in the purely random case. This supports the enhancement of $W_c$ in the case of a purely random potential by rare "ergodic spots," which do not occur in the quasi-periodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.

14 pages including appendix, 9 figures. Comments welcome