https://hal-polytechnique.archives-ouvertes.fr/hal-03539699Liu, TongTongLiuXia, XuXuXiaLonghi, StefanoStefanoLonghi IFISC (CSIC-UIB) - Instituto de fisic Interdisciplinar y Sistemas ComplejosSanchez-Palencia, LaurentLaurentSanchez-PalenciaCPHT - Centre de Physique Théorique [Palaiseau] - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueAnomalous mobility edges in one-dimensional quasiperiodic modelsHAL CCSD2022[PHYS.COND.GAS] Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas]Sanchez-Palencia, Laurent2022-01-21 22:30:592023-02-07 14:45:182022-01-21 22:30:59enJournal articles10.21468/SciPostPhys.12.1.0271Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate energy intervals where all states are localized from energy intervals where all states are critical in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite energy interval where all states are critical. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.