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We study the spectral and wavefunction properties of a one-dimensionalincommensurate system with p-wave pairing and unveil that the systemdemonstrates a series of particular properties in its ciritical region. Bystudying the spectral statistics, we show that the bandwidth distribution andlevel spacing distribution in the critical region follow inverse power laws,which however break down in the extended and localized regions. By performing afinite-size scaling analysis, we can obtain some critical exponents of thesystem and find these exponents fulfilling a hyperscaling law in the wholecritical region. We also carry out a multifractal analysis on system'swavefuntions by using a box-counting method and unveil the wavefuntionsdisplaying different behaviors in the critical, extended and localized regions.

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