  Flat, non-dispersive bands and topological phase transition in multiple
Su-Schrieffer-Heeger (SSH) chains, cross-linked via periodically arranged nodal
points are explored within a tight binding framework. We give analytic
prescription, based on a real space decimation scheme, that extracts the energy
eigenvalues corresponding to the flat bands along with their degeneracy. The
topological phase transition is confirmed through the existence of quantized
Zak phase for all the Bloch bands, and the edge states that are protected by
chiral symmetry, consistent with the bulk-boundary correspondence. In addition
to the edge states, the entangled systems are shown to give rise to clusters of
localized eigenstates in the bulk of the system, in contrast to a purely one
dimensional SSH system.
