Subsystem localization

• URL: http://arxiv.org/abs/2505.17876v3
• Date: Mon, 22 Sep 2025 21:36:21 GMT
• Title: Subsystem localization
• Authors: Arpita Goswami, Pallabi Chatterjee, Ranjan Modak, Shaon Sahoo,
• Abstract summary: We consider a ladder system where one leg, referred to as the bath", is governed by an Aubry-Andr'e type Hamiltonian.<n>We investigate the localization properties in the subsystem induced by its coupling to the bath.<n>An analysis of the projected wavepacket dynamics in the subsystem shows that the delocalized phase exhibits a ballistic behavior.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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 $t'/V \ll 1$, 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-Andr\'{e} (GAA) model.

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