



01902nas a2200157   4500008004100000245011500041210006900156260001500225520137700240100001801617700001301635700001701648700001901665700002301684856003701707       2019                        eng d00aButterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization0 aButterfly effect in interacting AubryAndre model thermalization   c02/19/20193 a<p>The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.</p>1 aXu, Shenglong1 aLi, Xiao1 aHsu, Yi-Ting1 aSwingle, Brian1 aSarma, Sankar, Das  uhttps://arxiv.org/abs/1902.07199