Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing

Abstract

We study the spectral and wavefunction properties of a one-dimensional incommensuratesystem with p-wave pairing and unveil that the system demonstrates a series of particularproperties in its ciritical region. By studying the spectral statistics, we show that thebandwidth distribution and level spacing distribution in the critical region followinverse power laws, which however break down in the extended and localized regions. Byperforming a finite-size scaling analysis, we can obtain some critical exponents of thesystem and find these exponents fulfilling a hyperscaling law in the whole criticalregion. We also carry out a multifractal analysis on system’s wavefuntions by using abox-counting method and unveil the wavefuntions displaying different behaviors in thecritical, extended and localized regions.