Subsystem localization in a two-leg ladder system

Arpita Goswami; Pallabi Chatterjee; Ranjan Modak; Shaon Sahoo

doi:10.1103/95t3-6qd4

paper

Subsystem localization in a two-leg ladder system

arXiv:2505.17876 · doi:10.1103/95t3-6qd4

Abstract

We consider a ladder system where one leg, referred to as the ``bath", is governed by an Aubry-André (AA) type Hamiltonian, while the other leg, termed the ``subsystem", 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 shows 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 $V$ . The fractal phase also appears in a narrow region along the boundary between the delocalized and localized phases. An analysis of the projected wavepacket dynamics in the subsystem shows that the delocalized phase exhibits a ballistic behavior, whereas the weakly delocalized phase is subdiffusive. Interestingly, the narrow fractal phase shows a super- to subdiffusive behavior as we go from the delocalized to localized phase. 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 an anomalous crossover regime where the system can be super- or subdiffusive. Beyond the ballistic phase observed at low $V$ , we also identify a superdiffusive regime emerging in the limit $t^{'} / V ≪ 1$ , which continuously approaches the ballistic behavior as $t^{'} \to 0$ . Finally, in some limiting scenario, we also establish a mapping between our ladder system and a well-studied one-dimensional generalized Aubry-André (GAA) model.

18 pages, 24 figures

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