Spectral Properties of Three Dimensional Layered Quantum Hall Systems

TL;DR

This paper numerically studies the spectral statistics of a 3D layered quantum Hall system, analyzing critical exponents, level spacing, and spectral compressibility to understand its spectral properties.

Contribution

It provides new numerical insights into the spectral statistics and critical behavior of three-dimensional layered quantum Hall systems, including verification of theoretical relations.

Findings

Tail of level spacing distribution decays exponentially

Spectral compressibility at criticality matches theoretical predictions

Critical exponent determined for various interlayer couplings

Abstract

We investigate the spectral statistics of a network model for a three dimensional layered quantum Hall system numerically. The scaling of the quantity $J_0={1/2}< s^2>$ is used to determine the critical exponent $\nu$ for several interlayer coupling strengths. Furthermore, we determine the level spacing distribution $P(s)$ as well as the spectral compressibility $\chi$ at criticality. We show that the tail of $P(s)$ decays as $\exp(-\kappa s)$ with $\kappa=1/(2\chi)$ and also numerically verify the equation $\chi=(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the spatial dimension.