Blog
About

5
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

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

      Preprint

      , , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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.

          Related collections

          Most cited references 30

          • Record: found
          • Abstract: not found
          • Article: not found

          Electrical resistance of disordered one-dimensional lattices

           Rolf Landauer (2006)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Relation between conductivity and transmission matrix

              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Observation of many-body localization of interacting fermions in a quasi-random optical lattice

              We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.
                Bookmark

                Author and article information

                Journal
                30 October 2018
                1810.12931

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                82D30
                13 pages, 6 figures
                cond-mat.dis-nn

                Theoretical physics

                Comments

                Comment on this article