  The interface between two materials described by spectrally gapped
Hamiltonians is expected to host an in-gap interface mode, whenever a certain
topological invariant changes across the interface. We provide a precise
statement of this bulk-interface correspondence, and its rigorous
justification. The correspondence applies to continuum and lattice models of
interfaces between one-dimensional materials with inversion symmetry, with
dislocation models being of particular interest. For continuum models, the
analysis of the parity of the "edge" Bloch modes is the key component in our
argument, while for the lattice models, the relative Zak phase and index theory
are.
