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

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 Znidaric 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.

Automated summary

Transport in a boundary-driven Anderson insulator was studied, showing a transition from diffusive to subdiffusive spin transport below a critical density of dephasing sites. The critical properties of this transition in two different models were interpreted in terms of Griffiths effects, with the interplay of characteristic disorder, dephasing, and percolation problem defining the finite-size scaling. It was conjectured that the logarithmic growth of large, rare insulating regions may be responsible for the absence of heavy-tailed resistance distributions in subdiffusive interacting systems.