We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw-Rebbi (JR) models. We show that time-reversal (T), charge-conjugation (C), parity (P), and discrete internal field rotation ([Formula: see text]) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the [Formula: see text] rotation symmetry, whereas it shows chiral solitons with the broken [Formula: see text] rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only [Formula: see text] rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced [Formula: see text] rotation symmetry. Moreover, we find that the nonchiral solitons have C, P symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that T, C, P symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.
© 2021. The Author(s).