  We explore nonadiabatic quantum phase transitions in an Ising spin chain with
a linearly time-dependent transverse field and two different spins per unit
cell. Such a spin system passes through critical points with gapless
excitations, which support nonadiabatic transitions. Nevertheless, we find that
the excitations on one of the chain sub-lattices are suppressed in the
nearly-adiabatic regime exponentially. Thus, we reveal a coherent mechanism to
induce exponentially large density separation for different quasiparticles.
