  Disordered quantum systems feature an energy scale know as the Thouless
energy. For energy ranges below this scale, the properties of the energy
spectrum can be described by random matrix theory. Above this scale a different
behavior sets in. For a metallic system it has been long ago shown by Altshuler
and Shklovskii that the number variance should increase as a power law with a
power dependent only on the dimensionality of the system. Although tantalizing
hints for this behavior have been seen in previous numerical studies, it is
quite difficult to verify this prediction using the standard local unfolding
methods. Here we use a different unfolding method, i.e., the singular value
decomposition, and establish a connection between the power law behavior of the
scree plot (the singular values ranked by their amplitude) and the power law
behavior of the number variance. Thus we are able to numerically verify the
Altshuler and Shklovskii's prediction for disordered $3D$, $4D$, and $5D$
single-electron Anderson models on square lattices in the metallic regime. The
same method could be applied to systems such as the Sachdev-Ye-Kitaev model and
various interacting many body models for which the many body localization
occurs. It has been recently reported that such systems exhibit a Thouless
energy and analyzing the spectrum's behavior on larger scales is of much
current interest.
