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We study transport in a one-dimensional boundary-driven Anderson insulator(the XX spin chain with onsite disorder) with randomly positioned onsitedephasing, observing a transition from diffusive to subdiffusive spin transportbelow a critical density of sites with dephasing. This model is intended tomimic the passage of an excitation through (many-body) insulating regions orergodic bubbles, therefore providing a toy model for the diffusion-subdiffusiontransition observed in the disordered Heisenberg model [1]. We also present theexact solution of a semiclassical model of conductors and insulators introducedin Ref. 2, which exhibits both diffusive and subdiffusive phases, andqualitatively reproduces the results of the quantum system. The criticalproperties of both models, when passing from diffusion to subdiffusion, areinterpreted in terms of "Griffiths effects". We show that the finite-sizescaling comes from the interplay of three characteristic lengths: oneassociated with disorder (the localization length), one with dephasing, and thethird with the percolation problem defining large, rare, insulating regions. Weconjecture that the latter, which grows logarithmically with system size, maypotentially be responsible for the fact that heavy-tailed resistancedistributions typical of Griffiths effects have not been observed insubdiffusive interacting systems.

physical review. b./physical review. b

Subdiffusion in a 1D Anderson insulator with random dephasing:  Finite-size scaling, Griffiths effects, and possible implications for  many-body localization