Localization in one-dimensional Soukoulis-Economou model with incommensurate potentials

Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

“…The variations of QFI with respect to E β in these bands are similar and show roughly sizeindependent. The eigenstates in the 7 th − 9 th bands are the localized states, which is in agreement with all the existing results about the three bands [37][38][39][40][41][42][43][44]. In a rough sense, the global mobility edges between the 6 th and 7 th bands show the mixed characteristics of extended states and localized states, and thus represent the fingerprints separating the two types of states in this specific model.…”

“…In the present calculation, we take V 0 = 1.9, V 1 = 1 3 and Q = 0.7 as given in Refs [37][38][39][40][41][42][43][44], so that a comprehensive comparison with those results in literature. This model was numerically solved by Soukoulis and Economou, and the main feature is a 9-band energy spectrum structure [37].…”

“…However, the locations of mobility edges are authorsdependent, which have been summarized in Ref. [39]. In detail, by studying the transmission coefficients and spatial behaviors of the eigenstates, a global mobility edge separating the 6 th and 7 th bands was claimed [37].…”

“…In this work, from the QFI perspective, we focus on the localization transitions in three well known one-dimensional tight-binding quantum models, i.e. the Aubry-André model [36], the t 1 − t 2 model [4] and the Soukoulis-Economou (S-E) model [37][38][39][40][41][42][43][44]. It will be demonstrated that the QFI in characterizing these localization transitions is highly appreciated.…”

Directional Scaling Symmetry of High-symmetry Two-dimensional Lattices

“…found and proved the existence of directional scaling symmetry for the equilateral triangular lattice (thus also the honeycomb lattice), and the square lattice. With the drag center set on a lattice point, in the case of equilateral triangular lattice, the direction of scaling symmetry is at 15°with regard to the side of the unit triangle, and the scale factor is7 4 , while in the case of square lattice, the direction of scaling symmetry is at 22.5°with regard to the side of the unit square triangle, and the scale factor is3 In both cases the scaling transformation can be performed repeatedly.The proof of the directional scaling symmetry for 2D lattices may suggest directional scaling symmetry for 3D cubic and rhombic lattices, which is an open question that we will bet on a positive answer. With the current work we want to call the attention to this directional scaling symmetry for the equilateral triangular lattice and square lattice, which is expected to have some impact on the various physics problems, particularly in statistical physics, condensed matter physics, quantum field theory, etc., modeled on such lattices.…”