  Nodal line in parameter space, at which the energy gap closes up, can either
be the boundary separating two topological quantum phases or two conventional
phases. We study the topological feature of nodal line in parameter space via a
dimerized Kitaev spin chain with staggered transverse field, which can be
mapped onto the system of dimerized spinless fermions with p-wave
superconductivity. The quantum phase boundaries are straight crossing
degeneracy lines in 3D parameter space. We show that the nodal line acts as a
vortex filament associated with a vector field, which is generated from the Zak
phase of Bogoliubov-de Gennes band. We also investigate the topological
invariant in Majorana fermion representation for open chain. The Majorana edge
modes are not zero mode, but is still protected by energy gap. The exact
mid-gap states of the Majorana lattice allows to obtain the corresponding
Majorana probability distribution for whole 3D parameter space, which can
establish a scalar field to identify the topological feature of the nodal
lines. Furthermore, when we switch on a weak tunneling between two ends of the
Majorana lattice, the topological invariants of the nodal lines can be obtained
by the pumped Majorana probability from an adiabatic passage encircling the
lines. Numerical simulations of quasi-adiabatic time evolution is performed in
small system. We compute the current to monitor the transport of Majorana
fermion, which exhibits evident character of topological pumping. Our results
link the bulk topological invariant to the dynamical behavior of Majorana edge
mode, extending the concept of bulk-edge correspondence.
