Transport in the non-ergodic extended phase of interacting quasiperiodic systems

TL;DR

This paper investigates the non-ergodic extended phase in a quasiperiodic interacting fermion system, revealing sub-diffusive transport properties distinct from thermal and localized phases.

Contribution

It provides a detailed analysis of the spectral statistics and transport in the non-ergodic extended phase, highlighting its unique sub-diffusive behavior.

Findings

Non-ergodic extended phase exhibits sub-diffusive transport.

Spectral statistics are consistent with this sub-diffusive behavior.

Transport is diffusive in the thermal phase and blocked in the MBL phase.

Abstract

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 ETH (eigenstate thermalization hypothesis) obeying (thermal), localized and ETH violating (many body localized) and extended and ETH violating (non-ergodic extended). Here we investigate the non-ergodic extended phase from the point of view of level spacing statistics and charge transport. We calculate the dc conductivity and the low frequency conductivity $\sigma(\omega)$ and show that both are consistent with sub-diffusive transport. This is contrasted with diffusive transport in the thermal phase and blocked transport in the MBL phase.