Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay

Understand

We investigate charge relaxation in quantum-wires of spin-less disordered fermions ($t{-}V$-model).

• Our observable is the time-dependent density propagator, $\Pi_{\varepsilon}(x,t)$, calculated in windows of different energy density, $\varepsilon$, of the many-body Hamiltonian and at different disorder strengths, $W$, not exceeding the critical value $W_\text{c}$.
• The width $\Delta x_\varepsilon(t)$ of $\Pi_\varepsilon(x,t)$ exhibits a behavior $d\ln \Delta x_\varepsilon(t) / d\ln t {=} \beta_\varepsilon(t)$, where the exponent function $\beta_\varepsilon(t){\lesssim}1/2$ is seen to depend strongly on $L$ at all investigated parameter combinations.
• (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that $\beta_\varepsilon{<}1/2$ in large window of times.