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This theoretical study establishes a rigorous framework for engineering exact mobility edges in quasiperiodic Aharonov-Bohm chains using synthetic magnetic flux. By analytically deriving expressions for these edges, the work demonstrates how controllable transitions between critical and extended states can be realized in platforms like superconducting quantum circuits and photonic waveguides. The findings offer a distinct mechanism for manipulating localization phenomena that differs from conventional off-diagonal models.
Engineering exact mobility edges in quasiperiodic Aharonov-Bohm chains
arXiv:2608.22264v1 Announce Type: cross Abstract: We investigate localization phenomena and exact mobility edges in a quasiperiodic Aharonov-Bohm chain, where the 1D canonical diagonal and off-diagonal Aubry-Andr\'{e}-Harper models are laterally coupled to an auxiliary sublattice threaded by a synthetic magnetic flux. By analytically computing the Lyapunov exponent via Avila's global theory of one-frequency Schr\"{o}dinger operators, we derive exact expressions for mobility edges. In the diagonal limit, the coupling to the auxiliary sublattice generates hyperbolic mobility edges that exhibit a sign-changing divergence and can be continuously tuned by the magnetic flux. In the off-diagonal regime, the interference between quasiperiodic hopping and indirect tunneling through the auxiliary sublattice gives rise to exact anomalous mobility edges that separate critical and extended states. Critical states and anomalous mobility edges emerge even in the absence of incommensurately distributed zeros in the hopping modulation, a behavior distinct from that of conventional off-diagonal models. Our results establish a rigorous theoretical framework for engineering controllable mobility edges, with the synthetic flux providing a tunable experimental knob that paves the way for realizations in platforms such as superconducting quantum circuits and photonic waveguides.
Abstract:We investigate localization phenomena and exact mobility edges in a quasiperiodic Aharonov-Bohm chain, where the 1D canonical diagonal and off-diagonal Aubry-André-Harper models are laterally coupled to an auxiliary sublattice threaded by a synthetic magnetic flux. By analytically computing the Lyapunov exponent via Avila's global theory of one-frequency Schrödinger operators, we derive exact expressions for mobility edges. In the diagonal limit, the coupling to the auxiliary sublattice generates hyperbolic mobility edges that exhibit a sign-changing divergence and can be continuously tuned by the magnetic flux. In the off-diagonal regime, the interference between quasiperiodic hopping and indirect tunneling through the auxiliary sublattice gives rise to exact anomalous mobility edges that separate critical and extended states. Critical states and anomalous mobility edges emerge even in the absence of incommensurately distributed zeros in the hopping modulation, a behavior distinct from that of conventional off-diagonal models. Our results establish a rigorous theoretical framework for engineering controllable mobility edges, with the synthetic flux providing a tunable experimental knob that paves the way for realizations in platforms such as superconducting quantum circuits and photonic waveguides.
Comments are welcomed! Accepted by PRB
Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
arXiv:2608.22264 [cond-mat.dis-nn]
(or arXiv:2608.22264v1 [cond-mat.dis-nn] for this version)
https://doi.org/10.48550/arXiv.2608.22264 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
https://doi.org/10.1103/h5m2-dr3l Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 294 words
