  We derive an exactly solvable one-dimensional (1D) spin model from the
three-band Hubbard model with a strong spin-orbit coupling by introducing U(1)
gauge fields to the isospin states. We find that it has a topological
nontrivial phase characterized by Majorana end modes which are protected by a
new Z_2 topological invariant related to the parity of the lattice sites (odd
or even number of sites) in the spin chain. With the protection of this Z_2
topological invariant, a novel braiding of two Majorana edge states in this
strictly geometric 1D chain is realized. We also discuss the possible
realization of the gauge fields.
