  We use multi-band SSH models to demonstrate a prescription for calculating
the correct Zak phase and winding number of multi-band systems. We verify our
prescription by comparing the resultant winding number of a four-band SSH model
with the edge states of a semi-infinite chain which we find by solving the
equation of motion. We then also carry out an extensive comparison with the
numerical results obtained by solving the matrix eigenvalue problem of finite
chains with various number of sites. As a double check of our prescription, we
also confirm the bulk edge correspondence in a six-band SSH model. Similar to
the usual SSH model, the winding numbers associated to the left and right
boundaries in a finite chain may be different if space inversion symmetry is
violated in the system. We believe the prescription we propose here may also be
applied to other 1D multi-band systems.
