  We study theoretically the topological quantum phase transition in Cavity QED
lattice. We predict the condition for non-topological phase to the topological
phase transition conditions for three different model Hamiltonians in cavity
QED lattice. We study these topological quantum phase transition through
winding number, which is a topological invariant quantity. We argue that the
appearance of topological phase in these systems where the discrete Z 2
symmetry broken. We show that the non-topological state is the vacuum state of
the system where each cavity contains fermionic type excitations from
light-matter interaction whereas the topological state of system contains
Majorana modes of excitations at the end cavity of the lattice.
