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Subsystem localization in a two-leg ladder system
Statistical Mechanics · Submitted 23 May 2025
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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 $V$.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | method 0.53 | 0.34 | 0.03 | asserted 0.91 |
| s1 | We investigate the localization properties in the subsystem induced by its coupling to the bath. | contribution 0.99 | 0.85 | 0.04 | unclear 0.63 |
| s2 | 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 $V$. | result 1.00 | 0.93 | 0.42 | asserted 1.00 |
| s3 | The fractal phase also appears in a narrow region along the boundary between the delocalized and localized phases. | result 1.00 | 0.89 | 0.06 | asserted 1.00 |
| s4 | 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. | result 0.98 | 0.93 | 0.11 | asserted 1.00 |
| s5 | Interestingly, the narrow fractal phase shows a super- to subdiffusive behavior as we go from the delocalized to localized phase. | result 1.00 | 0.91 | 0.10 | asserted 1.00 |
| s6 | 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 $V$. | result 1.00 | 0.95 | 0.11 | asserted 1.00 |
| s7 | Between those two phases, there is also an anomalous crossover regime where the system can be super- or subdiffusive. | result 1.00 | 0.93 | 0.07 | asserted 0.85 |
| s8 | 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 $t' \to 0$. | result 1.00 | 0.93 | 0.11 | asserted 1.00 |
| s9 | 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. | result 0.65 | 0.88 | 0.08 | asserted 0.96 |
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Original 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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Finally, in some limiting scenario, we also establish a mapping between our system and a well-studied one-dimensional generalized Aubry-André (GAA) model, which also exhibits similar ballistic, superdiffusive, and subdiffusive phases, as reported recently [ref] .
Emergence of distinct exact mobility edges in a quasiperiodic chain · Introduction · 0.90
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