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Spectral Properties of Three Dimensional Layered Quantum Hall Systems

Marcus Metzler
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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 $ν$ for several interlayer coupling strengths. Furthermore, we determine the level spacing distribution $P(s)$ as well as the spectral compressibility $χ$ at criticality. We show that the tail of $P(s)$ decays as $\exp(-κs)$ with $κ=1/(2χ)$ and also numerically verify the equation $χ=(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the spatial dimension.

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Marcus Metzler. 1998-09-25. Spectral Properties of Three Dimensional Layered Quantum Hall Systems. https://doi.org/10.1143/jpsj.67.4006

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