On the size scaling of the nearest level spacing at criticality

TL;DR

This paper confirms that the size scaling of the nearest level spacing at criticality follows the same power-law as in extended and critical phases, supporting a conjecture about spectral properties at phase transitions.

Contribution

The study provides numerical evidence that the size scaling exponent of the nearest level spacing at criticality matches that of the bare level spacing, validating a theoretical conjecture.

Findings

Scaling exponent matches that of bare level spacing

Supports the conjecture about spectral scaling at criticality

Applicable to models with long-range interactions

Abstract

It is conjectured that the size scaling of the nearest level spacing in the critical spectral region, $S(N)\propto N^{-\lambda}$, remains qualitatively the same within phases of extended and critical states. The exponent $\lambda$ is therefore identical to that for the bare level spacing (at zero disorder). Our calculation of the scaling for the one-dimensional model with diagonal disorder and long-range power-like interaction confirms the conjecture.