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Working in the context of the Su-Schreiffer-Heeger (SSH) model, the effect oftopological transitions on the structure and properties of bulk position-spacewavefunctions is studied for a particle undergoing a quantum walk in aone-dimensional lattice. In particular, we consider what happens when thewavefunction reaches a boundary at which the Hamiltonian changes suddenly fromone topological phase to another. An exact solution is constructed for thewavefunction on both sides of the boundary. Under some conditions, it is foundthat the probability of transition into the region of the second, topologicallydistinct Hamiltonian is strongly suppressed. When the boundary is encountered,the wavefunctions tend to be strongly reflected, and by appropriate choice ofsystem parameters leakage into the second region can be made negligible.Therefore, it is possible to arrange a high degree of bulk wavefunctionlocalization within in each region. This `topologically-assisted' suppressionof transitions, although not of direct topological origin itself, exists onlybecause of the presence of a change in the topological properties of theHamiltonian. We give a quantitative examination of the reflection andtransmission coefficients of incident waves at the boundary between regions ofdifferent winding number.

Topological Transitions and Bulk Wavefunctions in the SSH Model