Subsystem localization

Abstract: We consider a ladder system where one leg, referred to as the bath", is governed by an Aubry-Andr\'{e} (AA) type Hamiltonian, while the other leg, termed thesubsystem", follows a standard tight-binding Hamiltonian. We investigate the localization properties in the subsystem induced by its coupling to the bath. For the coupling strength larger than a critical value ($t'>t'_c$), the analysis of the static properties show that there are three distinct phases as the AA potential strength $V$ is varied: a fully delocalized phase at low $V$, a localized phase at intermediate $V$, and a weakly delocalized (fractal) phase at large $V$. An analysis of the wavepacket dynamics shows that the delocalized phase exhibits a ballistic behavior, whereas the weakly delocalized phase is subdiffusive. Interestingly, we also find a superdiffusive narrow crossover regime along the line separating the delocalized and localized phases. When $t'<t'_c$, the intermediate localized phase disappears, and we find a delocalized (ballistic) phase at low $V$ and a weakly delocalized (subdiffusive) phase at large $V$. Between those two phases, there is also a crossover regime where the system can be super- or subdiffusive. Finally, in some limiting scenario, we also establish a mapping between our ladder system and a well-studied one-dimensional generalized Aubry-Andr\'{e} (GAA) model.