Level-spectra Statistics in Planar Fractal Tight-Binding Models
arXiv:2212.13972 · doi:10.1103/PhysRevB.107.115424
Abstract
In this communication, we study the level-spectra statistics when a noninteracting electron gas is confined in \textit{Sierpiński Carpet} (\textit{SC}) lattices. These \textit{SC} lattices are constructed under two representative patterns of the and patterns, and classified into two subclass lattices by the area-perimeter scaling law. By the singularly continuous spectra and critical traits using two level-statistic tools\iffalse the nearest spacing distribution and alternative gap-ratio distribution\fi, we ascertain that both obey the critical phase due to broken translation symmetry and the long-range order of scaling symmetry. The Wigner-like conjecture is confirmed numerically since both belong to the Gaussian orthogonal ensemble. An analogy was observed in a quasiperiodic lattice~\cite{Zhong1998Level}. In addition, this critical phase isolates the crucial behavior near the metal-insulator transition edge in Anderson model. The lattice topology of the self-similarity feature can induce level clustering behavior.
arXiv comment11 pages, 6 figures, 2 Tables
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