  We investigate continuous-time quantum walks of two fermionic atoms loaded in
one-dimensional optical lattices with on-site interaction and subjected to a
Zeeman field. The quantum walks are accompanied by spin-flipping processes. We
calculate the time-dependent density distributions of the two fermions with
opposite spins which are initially positioned on the center site by means of
exact numerical method. Besides the usual fast linear expansion behavior, we
find an interesting spin-flipping induced localization in the time-evolution of
density distributions. We show that the fast linear expansion behavior could be
restored by simply ramping on the Zeeman field or further increasing the
spin-flipping strength. The intrinsic origin of this exotic phenomenon is
attributed to the emergence of a flat band in the single particle spectrum of
the system. Furthermore, we investigate the effect of on-site interaction on
the dynamics of the quantum walkers. The two-particle correlations are
calculated and signal of localization is also shown therein. A simple potential
experimental application of this interesting phenomenon is proposed.
