Butterfly effect in interacting Aubry-Andre model: Thermalization, slow scrambling, and many-body localization

Abstract

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. arXiv:1902.07199v1 [cond-mat.str-el]

Many-body localization in a quasiperiodic Fibonacci chain

“…In the ETH phase (h ≤ h * ), we observe a sublinear scaling of the natural orbitals, compatible with a survival of the free fermions multifractality. Moreover, we find sub-diffusive dynamics for both imbalance and growth of entanglement entropy, a result which is a bit surprising -but in line with some results on the quasiperiodic Aubry-André model [37,71,83,84] -as the Fibonacci potential is free of rare Griffiths regions, which are usually thought [15,16] to cause such power-law behaviors.…”

“…Alternatively, Griffiths effects in the choice of the initial state have been proposed [71] to account for the slow dynamics. Note also the recent work [84], which reports the existence of a "slow" phase with respect to the spreading of information in the neighborhood of the Aubry-André ETH/MBL transition.…”

Diffusive transport in a quasiperiodic Fibonacci chain: Absence of many-body localization at weak interactions

“…In the absence of rare regions (like in quasiperiodic systems), however, one therefore expects only diffusive transport all the way to the MBL transition. Indeed for the interacting AAH model [40][41][42][43][44][45][46][47][48][49][50][51][52][53] , this was to a certain extend observed 48,50 , see however e.g. Refs.…”

Emergence of anomalous dynamics from the underlying singular continuous spectrum in interacting many-body systems

“…The model has been realized with ultracold atoms loaded in a bichromatic optical lattice [13][14][15]. Due to the interplay of quasiperiodicity and interparticle interaction, a nontrivial phase diagram arises [16][17][18], together with the appearance of a mobility edge [19][20][21], a many-body-localized phase [14,15,[22][23][24], and instabilities [25]. The problem of how interactions modify the properties of SC spectra has been addressed in the seminal work [26], with the conclusion that they would destroy SC SPES.…”