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

## TL;DR

This paper investigates many-body localization in a quasi-periodic spin chain, revealing how the periodicity affects the critical disorder strength and showing that finite-size effects are weaker than in random systems.

## Contribution

It provides new insights into how the choice of quasi-periodic potential influences the localization transition and finite-size effects in many-body systems.

## Key findings

- Critical disorder W_c ≈ 4.8 for inverse golden ratio periodicity
- Higher critical disorder W_c ≈ 7.8 for different periodicity
- Finite-size effects are weaker than in random disorder cases

## Abstract

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 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.