  Topological index of a system specifies gross features of the system.
However, in situations such as strong disorder where by level repulsion
mechanism the spectral gap is closed, the topological indices are not
well-defined. In this paper, we show that the localization length of zero modes
determined from appropriate use of transfer matrix method reveals much more
information than the topological index. The localization length can provide not
only information about the topological index of the Hamiltonian itself, but it
can also provide information about the topological indices of the related
Hamiltonians. As a case study, we study a generalized XY model (2XY model) plus
a generalized Dziyaloshinskii-Moriya-like (DM) interaction that after
fermionization breaks the time-reversal invariance and is parameterized by
$\phi$. The {\em parent} Hamiltonian at $\phi=0$ which belongs to BDI class is
indexed by integer winding number while the $\phi\ne 0$ {\em daughter}
Hamiltonian which belongs to class D is specified by a $Z_2$ index $\nu=\pm 1$.
We show that the localization length in addition to determining the $Z_2$ can
count the number of Majorana zero modes left over at the boundary of the
daughter Hamiltonian -- which are not protected by winding number anymore.
Therefore the localization length outperforms the standard topological indices
in two respects: (i) it is much faster and more accurate to calculate and (ii)
it can count the winding number of the parent Hamiltonian by looking into the
edges of the daughter Hamiltonian.
