Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

Abstract

There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport (3d); precisely at the transition, the system displays sub-diffusive critical states. We calculate the beta function $\beta (g)=dln(g)/dln(L)$ and show that, in 1d and 2d, single-parameter scaling is unable to describe the transition. Further- more, the conductances show strong non-monotonic variations with L and an intricate structure of resonant peaks and subpeaks. In 1d the positions of these peaks can be related precisely to the prop- erties of the number that characterizes the quasiperiodicity of the potential; and the L-dependence of the Thouless conductance is multifractal. We find that, as d increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our results for $\beta (g)$ are reasonably well approximated by single-parameter scaling.

13 pages, 6 figures

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Cited by in corpus (22)

• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Moire Localization in Two Dimensional Quasi-Periodic Systems
• Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current
• Quantum dynamics in the interacting Fibonacci chain
• Localization Driven Quantum Sensing
• Quantum phase transition between hyperuniform density distributions
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Sub-diffusive phases in open clean long-range systems
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Quasidisorder Induced Topology
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Stark localization near Aubry-André criticality
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Read-out of Quasi-periodic Systems using Qubits
• Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-André Model
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Spectral form factor and energy correlations in banded random matrices
• Dephasing-enhanced performance in quasiperiodic thermal machines
• Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes