# Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion

## TL;DR

This study investigates electron transport in a one-dimensional quasiperiodic interacting system, revealing a transition from superdiffusive to subdiffusive behavior and discussing implications for many-body localization.

## Contribution

The paper combines numerical and renormalization-group methods to analyze transport in a nonintegrable quasiperiodic system, highlighting the absence of diffusion and the crossover in dynamical regimes.

## Key findings

- No diffusive transport observed in studied parameters.
- System exhibits a crossover from superdiffusion to subdiffusion.
- Results support the Griffiths picture of subdiffusion in many-body localization.

## Abstract

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.