Intermediate super-exponential localization with Aubry-André chains
arXiv:2304.14741 · doi:10.1103/PhysRevB.108.064204
Abstract
We demonstrate the existence of an intermediate super-exponential localization regime for eigenstates of the Aubry-André chain. In this regime, the eigenstates localize factorially similarly to the eigenstates of the Wannier-Stark ladder. The super-exponential decay emerges on intermediate length scales for large values of the -- the quasi-period of the Aubry-André potential. This intermediate localization is present both in the metallic and insulating phases of the system. In the insulating phase, the super-exponential localization is periodically interrupted by weaker decaying tails to form the conventional asymptotic exponential decay predicted for the Aubry-André model. In the metallic phase, the super-exponential localization happens for states with energies away from the center of the spectrum and is followed by a super-exponential growth into the next peak of the extended eigenstate. By adjusting the parameters it is possible to arbitrarily extend the validity of the super-exponential localization. A similar intermediate super-exponential localization regime is demonstrated in quasiperiodic discrete-time unitary maps.
arXiv comment9 pages, 9 figures. Comments are welcome
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