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

التفاصيل البيبلوغرافية
العنوان: Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
المؤلفون: Sutradhar, Jagannath, Mukerjee, Subroto, Pandit, Rahul, Banerjee, Sumilan
المصدر: Phys. Rev. B 99, 224204 (2019)
سنة النشر: 2018
المجموعة: Condensed Matter
مصطلحات موضوعية: Condensed Matter - Disordered Systems and Neural Networks, 82D30
الوصف: 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.
Comment: 13 pages, 6 figures
نوع الوثيقة: Working Paper
DOI: 10.1103/PhysRevB.99.224204
URL الوصول: http://arxiv.org/abs/1810.12931
رقم الأكسشن: edsarx.1810.12931
قاعدة البيانات: arXiv
الوصف
DOI:10.1103/PhysRevB.99.224204