We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single-particle mobility edge in the absence of interaction. For such systems, it has been shown that the many-body eigenstates can be of three different kinds: extended and eigenstate thermalization hypothesis (ETH) obeying (thermal), localized and ETH violating (many body localized), and extended and ETH violating (nonergodic extended). Here we investigate the nonergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low-frequency conductivity $\sigma \left(\omega \right)$ and show that both are consistent with subdiffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.

• Received 19 July 2020
• Revised 18 October 2020
• Accepted 19 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.224203