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arXiv:2106.11406 · Physical review. B./Physical review. B

Dephasing enhanced transport in boundary-driven quasiperiodic chains

Artur M. Lacerda, John Goold, Gabriel Teixeira Landi

Published Nov 3, 2021• 1 citation
arXivHTMLPDF

Abstract

We study dephasing enhanced transport in boundary-driven quasiperiodic systems. Specifically, we consider dephasing modeled by current-preserving Lindblad dissipators acting on the noninteracting Aubry-Andr\'e-Harper and Fibonacci bulk systems. The former is known to undergo a critical localization transition with a suppression of ballistic transport above a critical value of the potential. At the critical point, the presence of nonergodic extended states yields anomalous subdiffusion. The Fibonacci model, on the other hand, yields anomalous transport with a continuously varying exponent depending on the potential strength. By computing the covariance matrix in the nonequilibrium steady state, we show that sufficiently strong dephasing always renders the transport diffusive. The interplay between dephasing and quasiperiodicity gives rise to a maximum of the diffusion coefficient for finite dephasing, which suggests that the combination of quasiperiodic geometries and dephasing can be used to control noise enhanced transport.

DOI
10.1103/physrevb.104.174203

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We study dephasing enhanced transport in boundary-driven quasiperiodic systems. Specifically, we consider dephasing modeled by current-preserving Lindblad dissipators acting on the noninteracting Aubry-Andr'e-Harper and Fibonacci bulk systems. The former is known to undergo a critical localization transition with a suppression of ballistic transport above a critical value of the potential. At the critical point, the presence of nonergodic extended states yields anomalous subdiffusion. The Fibonacci model, on the other hand, yields anomalous transport with a continuously varying exponent depending on the potential strength. By computing the covariance matrix in the nonequilibrium steady state, we show that sufficiently strong dephasing always renders the transport diffusive. The interplay between dephasing and quasiperiodicity gives rise to a maximum of the diffusion coefficient for finite dephasing, which suggests that the combination of quasiperiodic geometries and dephasing can be used to control noise enhanced transport.
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 a random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small UUU always slows down the noninteracting 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.''
One dimensional quasiperiodic systems have been a vibrant topic of theorical research for physicists and mathematicians alike, owing to their highly non-trivial localization properties and the fractal nature of their energy spectrum.The most paradigmatic of such systems, the Aubry-André-Harper (AAH) model, is well known for suffering a localization transition when the potential strength is increased, in which its eigenstates go from extended to localized, similarly to Anderson phase transition which occurs in disordered three-dimensional systems.The localization of the eigenstates has dramatic effects in the transport regime of the system.In this dissertation, we used numerical simulations to study the transport properties of boundary-driven fermionic quantum chains subject to two choices for the on-site potential: the aforementioned AAH model and the Fibonacci model.The transport regime is classified via the scaling of the particle current with the system size in the non-equilibrium steady state (NESS), which we calculate numerically.Our main focus was the interplay between the quasiperiodic potential and dephasing noise.We showed that even though dephasing always leads to diffusive behaviour, the transport properties of the system are still visibly affected by localization properties of the eigenstates when the coupling to dephasing is small.This influence is reflected in the scaling of the diffusion constant with the coupling.In particular, we showed that, in the localized phase of the AAH model and in the subdifusive phase of the Fibonacci model, dephasing noise may actually lead to an enhanced transport, that is, a larger value of the current compared to the zero dephasing case.
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.
Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of Gtyp∼L−2\mathcal{G}_{\text{typ}}\sim L^{-2}Gtyp​∼L−2 with system size LLL. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.
We study a model of noninteracting spinless fermions coupled to local dephasing and boundary drive and described within a Lindblad master equation. The model features an interplay between infinite temperature thermalization due to bulk dephasing and a nonequilibrium stationary state due to the boundary drive and dissipation. We revisit the linear and nonlinear transport properties of the model, featuring a crossover from ballistic to diffusive scaling, and compute the spectral and occupation properties encoded in the single-particle Green's functions, that we compute exactly using the Lindblad equations of motion in spite of the interacting nature of the dephasing term. We show that the distribution function in the bulk of the system becomes frequency independent and flat, consistent with infinite temperature thermalization, while near the boundaries it retains strong nonequilibrium features that reflect the continuous injection and depletion of particles due to driving and dissipation.
Anderson localization and the mobility edge (ME) have been extensively studied in isolated aperiodic systems. Conventional theory suggests that dephasing and decoherence should disrupt localization and facilitate transport. In this work, we investigate localization behaviors in a dimerized off-diagonal Aubry-Andre-Harper (AAH) quasicrystal subject to on-site pure dephasing. In the strong-dephasing limit, we apply adiabatic elimination within the Lindblad master equation framework to derive an effective classical Markov transition matrix that governs the dissipative relaxation dynamics. Counterintuitively, we demonstrate that pure dephasing can induce distinct MEs, including both conventional MEs separating extended and localized states and anomalous MEs separating multifractal critical states from localized states, even when all eigenstates of the original closed coherent system are delocalized or multifractal. Using fractal dimension finite-size scaling, wave-packet spreading dynamics, and energy spectrum statistics, we numerically verify the coexistence of fully extended, multifractal critical, and localized regions within the relaxation spectrum of the dissipative system, and construct the global dissipative phase diagram. These findings reveal that dephasing can see as a powerful mechanism for controlling localization transitions, thus enhancing our understanding of dissipative quasicrystal systems.