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

• Published in: Physical review. B 2019-09, Vol.100 (10), Article 104203
• Main Authors: Doggen, Elmer V. H., Mirlin, Alexander D.
• Format: Article
• Language: English
• Subjects: Antiferromagnetism; Chains; Decay rate; Many body problem; Periodic variations; Size effects; Spin dynamics; Time dependence
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.100.104203

We study quench dynamics in an interacting spin chain with a quasiperiodic 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 Φ of the quasiperiodic field influences the dynamics. For Φ=(5−1)/2 (the inverse golden ratio) and interaction Δ=1, the model most frequently considered in the literature, we obtain the critical disorder Wc=4.8±0.5 in units where the noninteracting transition is at W=2. At the same time, for periodicity Φ=2/2 we obtain a considerably higher critical value, Wc=7.8±0.5. Finite-size effects on the critical disorder Wc are much weaker than in the purely random case. This supports the enhancement of Wc in the case of a purely random potential by rare "ergodic spots," which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.