Spectral Properties of Three Dimensional Layered Quantum Hall Systems

Details Spectral Properties of Three Dimensional Layered Quantum Hall Systems Spectral Properties of Three Dimensional Layered Quantum Hall Systems

1998-09-25

arxiv.org/abs/cond-mat/9809340v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 5 figures submitted to J. Phys. Soc. Jpn

Scientific paper

10.1143/JPSJ.67.4006

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.

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