We study topological properties of phase transition points of one-dimensional
topological quantum phase transitions by assigning winding numbers defined on
closed circles around the gap closing points in the parameter space of momentum
and a transition driving parameter, which overcomes the problem of ill
definition of winding numbers on the transition points. By applying our scheme
to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we
demonstrate that the topological phase transition can be well characterized by
winding numbers of transition points, which reflect the change of the winding
number of topologically different phases across the phase transition points.Comment: 5 pages, 5 figure
