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

Abstract

We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics, with agreeing diffusion constants. This must be contrasted to random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small U always slows down the non-interacting dynamics to subdiffusion, and is therefore unable to describe diffusion in an interacting quasiperiodic system. Finally, briefly exploring larger interactions we find a regime of interaction-induced subdiffusive dynamics, despite the on-site potential itself having no "rare-regions". arXiv:1905.03128v2 [cond-mat.str-el]

Transport in the nonergodic extended phase of interacting quasiperiodic systems

“…We thus provide evidence suggestive of subdiffusive transport even in the presence of a deterministic quasiperiodic potential which does not allow for Griffiths regions (which occur in the presence of random disorder), which we attribute to the presence of the nonergodic extended phase. A subdiffusive phase has also been reported in the interacting Aubry-André model near the critical region of the thermal-MBL transition [42] and in the Fibonacci model [44] in the presence of large interaction, while for small interaction the model shows only diffusive behavior. The Fibonacci model and the Aubry-André model also do not allow for the Griffiths scenario as rare regions of on-site potential do not appear.…”

“…The transport properties of one-dimensional systems are very interesting as there can be rich varieties of transport in one-dimensional systems depending on the underlying potential in both the interacting and noninteracting regimes [35][36][37][38][39][40][41][42][43][44]. In this paper we investigate the transport properties of the nonergodic extended phase in systems with a singleparticle mobility edge.…”

Phenomenology of anomalous transport in disordered one-dimensional systems

“…The scaling exponent of R is about γ ≈ 2.0 (which is slightly different than γ = 1/β − 1 ≈ 1.6 obtained from a wave-packet spreading in Ref. 42), however one should be aware that possible different scaling exponents could emerge using different sequences of L (see the Aubry-Andre case for an example 60 ). The additivity argument would therefore predict that x := R α with α = 1/γ ≈ 0.5 should be Gaussian distributed.…”

Periodically refreshed baths to simulate open quantum many-body dynamics

“…WhenĤ S describes an interacting quantum many-body system, even with the above rather mild assumptions, it remains an extremely challenging problem. Further assumptions are most often made to enable a Markovian description of the system's dynamics [24][25][26][27][28][29][30][31][32][33][34][56][57][58][59]. These descriptions are limited to either weak system-bath couplings or to infinite temperatures [51,60].…”

“…We show this by simulating the dynamics of interacting quantum many-body fermionic chains strongly coupled to two baths at different (finite) temperatures and chemical potentials, using one of these techniques [12][13][14]. Obtaining the numerically exact dynamics of interacting quantum many-body chains in such two-terminal setups has been an outstanding problem, despite its relevance in a wide range of contexts, such as quantum transport, localization, integrability breaking [24][25][26][27][28][29][30][31][32][33][34], quantum heat engines, and refrigerators [2]. Further, we discuss the relationship between our formalism and collisional (or repeated interaction) models [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], highlighting how our results extend these notions, significantly advancing this highly active field of research.…”