Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential

Understand

We investigate charge relaxation in disordered and quasi-periodic quantum-wires of spin-less fermions ($t{-}V$-model) at different inhomogeneity strength $W$ in the localized and nearly-localized regime.

• Our observable is the time-dependent density correlation function, $\Phi(x,t)$, at infinite temperature.
• We find that disordered and quasi-periodic models behave qualitatively similar: Although even at longest observation times the width $\Delta x(t)$ of $\Phi(x,t)$ does not exceed significantly the non-interacting localization length, $\xi_0$, strong finite-size effects are encountered.
• Our findings appear difficult to reconcile with the rare-region physics (Griffiths effects) that often is invoked as an explanation for the slow dynamics observed by us and earlier computational studies.