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Anomalous mobility edges in one-dimensional quasiperiodic models
by Tong Liu, Xu Xia, Stefano Longhi, Laurent Sanchez-Palencia
This is not the current version.
|As Contributors:||Laurent Sanchez-Palencia|
|Arxiv Link:||https://arxiv.org/abs/2105.04591v1 (pdf)|
|Date submitted:||2021-06-03 14:41|
|Submitted by:||Sanchez-Palencia, Laurent|
|Submitted to:||SciPost Physics|
Mobility 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 bands of localized states from bands of critical states 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 band of critical states. 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.
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Anonymous Report 1 on 2021-7-26 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2105.04591v1, delivered 2021-07-26, doi: 10.21468/SciPost.Report.3294
This is a very good study on the mobility edge in some 1D quasiperiodic models. The numerical investigation seems solid, and the results are very interesting.
The authors first analytically prove that for a specific model, only eigenstates with eigenenergies in between [-2,2] are non-localized. Since no extended state is allowed for unbounded potential, they further conclude that these eigenstates should be critical. Numerical calculations confirm their conclusion. They have also numerically investigated some other models, and generalize their conclusion.
I think this is an interesting work that definitely deserves to be published. I only have some minor suggestions for the authors (see the requested changes box).
(1) The authors claim that, in a sentence below Eq. (1), that the phase "theta" is irrelevant. This is, however, usually not entirely true in the investigation of localization physics in quasiperiodic models. One usually need to take the average of "\theta" to mimic the randomness of a genetic disorder. Although this average is usually more important in the extensive phase than the localized phase. I however wonder has this \theta dependency has been considered and investigated. I can see in Eq. (3) that the analytical analysis to some degree includes this average by the integration over \theta, so the question is more concerning on the numerical analysis.
(2) The energy gap is usually an important observable for the studies of localization. The gap ratio usually can give us information on whether the eigenenergies follows Gaussian Orthogonal Ensemble distribution or Poisson distribution. This is an important signature of an extensive/localized spectrum. For completeness, I suggest the authors carry out this analysis.
(3) This is a very minor problem, but I am a bit confused about the choice of their word "band". In the introduction, the third paragraph, the authors claim that "... can give rise to a full band of critical states ...". In condensed matter physics, a "band" usually refers to a set of eigenenergies that are close to each other, with a relatively large gap between the different bands. In Figure 1(b), one can see that the spectrum consists of multiple bands, and these bands can sometimes cross the mobility edge. Therefore, I think the term "band" might be a bit misleading. That being said, this seems to me only a problem of choice of word.