• Corpus ID: 251320351

A general approach to the exact localized transition points of 1D mosaic disorder models

@inproceedings{Liu2022AGA,
  title={A general approach to the exact localized transition points of 1D mosaic disorder models},
  author={Yanxia Liu},
  year={2022}
}
In this paper, we present a general relation between the mosaic and non-mosaic models, which can be used to obtain the exact solution for the former ones. This relation holds not only for the quasicrystal models, but also the Anderson models. Despite the different localization properties, the relationship between the models shares a unified form. Then we apply our method to the mosaic Anderson models and find that there is a discrete set of extended states. Moreover, we also give the general… 

Figures from this paper

References

SHOWING 1-10 OF 37 REFERENCES

Exact Mobility Edges in 1D Mosaic Lattices Inlaid with Slowly Varying Potentials

A family of 1D mosaic models inlaid with a slowly varying potential is proposed. Combining the asymptotic heuristic argument with the theory of trace map of transfer matrix, mobility edges (MEs), and

Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials

We study theoretically the localization properties of two distinct one-dimensional quasiperiodic lattice models with a single-particle mobility edge (SPME) separating extended and localized states in

Mobility edges in one-dimensional bichromatic incommensurate potentials

We theoretically study a one-dimensional (1D) mutually incommensurate bichromatic lattice system which has been implemented in ultracold atoms to study quantum localization. It has been universally

Self-consistent theory of mobility edges in quasiperiodic chains

The underlying theoretical framework introduced is model-independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems and results are shown to be in very good agreement with the exactly known mobility edges as well numerical results obtained from exact diagonalisation.

Nearest neighbor tight binding models with an exact mobility edge in one dimension.

This model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry, and introduces the typical density of states as an order parameter for localization in quasiperiodic systems.

Single-Particle Mobility Edge without Disorder

The existence of localization and mobility edges in one-dimensional lattices is commonly thought to depend on disorder (or quasidisorder). We investigate localization properties of a disorder-free

Majorana fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials.

A topological invariant derived from the equations of motion for Majorana modes is defined and employed to characterize the phase diagram for simple periodic structures and its general result is a relation between the normal state localization length.

Localization and adiabatic pumping in a generalized Aubry-André-Harper model

A generalization of the Aubry-Andre-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying

Metal-Insulator Transition and Scaling for Incommensurate Systems

Tight-binding models in one dimension with incommensurate potentials are studied. For the sinusoidal-potential model scaling of the spectrum is found numerically at the critical point, which

Localization in one-dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models

We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor,