Level-spectra Statistics in Planar Fractal Tight-Binding Models

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 $self$ and $gene$ 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.

11 pages, 6 figures, 2 Tables

References in corpus (7)

• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Thermodynamics of photons on fractals
• Critical eigenstates and their properties in one and two dimensional quasicrystals
• Optical conductivity of a quantum electron gas in a Sierpinski carpet
• Engineering light localization in a fractal waveguide network
• Linearized spectral decimation in fractals

Cited by in corpus (1)

• Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice