Spectral Properties of Three Dimensional Layered Quantum Hall Systems
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.