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

TL;DR

This paper investigates the spectral, wavefunction, and multifractal properties of a one-dimensional incommensurate p-wave superconducting chain, revealing critical behaviors and scaling laws at phase transitions.

Contribution

It provides a detailed analysis of spectral statistics, critical exponents, and multifractal wavefunction properties in a quasiperiodic p-wave chain, highlighting new insights into its critical phenomena.

Findings

Spectral statistics follow inverse power laws at criticality

Critical exponents satisfy a hyperscaling law

Wavefunctions exhibit multifractal behavior in the critical region

Abstract

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