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arXiv:2005.10835 · Physical review. B./Physical review. B

Nonequilibrium steady state phases of the interacting Aubry-André-Harper model

Yongchan Yoo, Junhyun Lee, Brian G. Swingle

Published Nov 23, 2020• 30 citations
arXivHTMLPDF

Abstract

Recent studies of quantum many-body dynamics uncover many intriguing phenomena of thermalization and localization in the presence of a quasiperiodic potential. In this paper, the authors study nonequilibrium steady states of the one-dimensional interacting Aubry-Andre-Harper model by taking advantage of tensor network-based algorithms. In a weak potential regime, they find a superdiffusive to subdiffusive transition in spin transport within the thermal phase. The correlation structure of the steady states derived from the quantum mutual information shows an unusual oscillation pattern before reaching the localization transition. Our results suggest a rich phase diagram for the model.

DOI
10.1103/physrevb.102.195142

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Reply to “Comment on ‘Nonequilibrium steady state phases of the interacting Aubry-André-Harper model' ”

Yongchan Yoo, Junhyun Lee, Brian G. Swingle

Received 13 April 2021Accepted 10 May 2021DOI:https://doi.org/10.1103/PhysRevB.103.237102©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMany-body localizationQuantum entanglementQuantum transportPhysical Systems1-dimensional spin chainsTechniquesTensor network methodsStatistical PhysicsCondensed Matter, Materials & Applied Physics

Physical review. B./Physical review. B•Jun 21, 2021•0 citations
Recent studies of quantum many-body dynamics uncover many intriguing phenomena of thermalization and localization in the presence of a quasiperiodic potential. In this paper, the authors study nonequilibrium steady states of the one-dimensional interacting Aubry-Andre-Harper model by taking advantage of tensor network-based algorithms. In a weak potential regime, they find a superdiffusive to subdiffusive transition in spin transport within the thermal phase. The correlation structure of the steady states derived from the quantum mutual information shows an unusual oscillation pattern before reaching the localization transition. Our results suggest a rich phase diagram for the model.
We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular, we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a viable experimental technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.
We investigate and map out the nonequilibrium phase diagram of a generalization of the well known Aubry-Andr\'e-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of the AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wave functions near the mobility edge of the GAAH model and the wave functions of the critical AAH model. By placing this model far from equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of nonequilibrium steady state (NESS) current, calculated by fully exact nonequilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a `critical' line separating regions of ballistic and localized transport. Like the critical point of the AAH model, current scales subdiffusively with system size on the `critical' line ($I\ensuremath{\sim}{N}^{\ensuremath{-}2\ifmmode\pm\else\textpm\fi{}0.1}$). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where $I\ensuremath{\sim}{N}^{\ensuremath{-}1.4\ifmmode\pm\else\textpm\fi{}0.05}$). All these results can be understood from the above-mentioned connection between states near the mobility edge of the GAAH model and those of the critical AAH model. A very interesting high temperature nonequilibrium phase diagram of the GAAH model emerges from our calculations.
Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in a one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no finite region of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.
Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.