Fractality in nonequilibrium steady states of quasiperiodic systems

Abstract

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 transparent and experimentally viable 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.

arXiv comment2 column format, 4+5.5+1 pages, 4+10 figures; v2 has more broccoli inside: further support for (i) fractality and scaling of various transport + steady state measures in generalized Fibonacci sequences, (ii) contrast between open vs. closed system dynamics

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Cited by in corpus (39)

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• Many-body localization in a quasiperiodic Fibonacci chain
• Quasiperiodic quantum heat engines with a mobility edge
• Non-power-law universality in one-dimensional quasicrystals
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
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• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
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• Quantum dynamics in the interacting Fibonacci chain
• Classifying transport behavior via current fluctuations in open quantum systems
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Dynamic scaling relation in quantum many-body systems
• Less is more: more scattering leading to less resistance
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• Destruction of Localization by Thermal Inclusions: Anomalous Transport and Griffiths Effects in the Anderson and André-Aubry-Harper Models
• Waiting-times statistics in boundary driven free fermion chains
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Critical behavior of the quasi-periodic quantum Ising chain
• An Extension of ETH to Non-Equilibrium Steady States
• Read-out of Quasi-periodic Systems using Qubits
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
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• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Diffusion and Thermalization in a Boundary-Driven Dephasing Model
• Quantum transport under oscillatory drive with disordered amplitude
• Transfer matrix approach to quantum systems subject to certain Lindblad evolution
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field
• Dephasing enhanced transport in boundary-driven quasiperiodic chains
• Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes
• Approaching the scaling limit of transport through lattices with dephasing
• Dephasing-enhanced performance in quasiperiodic thermal machines