2020/07/31 by Scott Richard Taylor, Scott R. Taylor, Antonello Scardicchio
Mathematics · Physics and Astronomy · #Anderson localization #Condensed matter physics #Dephasing #Ergodic theory #Mathematics #Percolation (cognitive psychology) #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Scaling #Statistical physics #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.103.184202
published as Phys. Rev. B 103, 184202 (2021) · 15 pages, 11 figures. Paper restructured and discussions extended
arxiv created 2021/02/06 · openalex created_date 2021/02/15 · openalex publication_date 2021/05/07 · arxiv updated 2021/05/12 · openalex updated_date 2026/08/05
We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. This model is intended to mimic the passage of an excitation through (many-body) insulating regions or ergodic bubbles, therefore providing a toy model for the diffusion-subdiffusion transition observed in the disordered Heisenberg model by \ifmmode \checkZ\else \vZ\finidari\ifmmode \checkc\else \vc\fi et al. [Phys. Rev. Lett. 117, 040601 (2016)]. We also present the exact solution of a semiclassical model of conductors and insulators introduced by Agarwal et al. [Phys. Rev. Lett. 114, 160401 (2015)], which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The critical properties of both models, when passing from diffusion to subdiffusion, are interpreted in terms of ``Griffiths effects.'' We show that the finite-size scaling comes from the interplay of three characteristic lengths: one associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. We conjecture that the latter, which grows logarithmically with system size, may potentially be responsible for the fact that heavy-tailed resistance distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.