Abstract
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 (Z_n) 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 Z_2 rotation symmetry, whereas it shows chiral solitons with the broken Z_2 rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only Z_2 rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced Z_4 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.
Highlights
We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw–Rebbi (JR) models
We find that the enhanced Z4 rotation symmetry supports the emergence of chiral and nonchiral solitons
In right chiral (RC) and left chiral (LC) soliton systems, C and P symmetries are broken because the bose fields deviate from the symmetry-invariant line, which naturally endows the chirality to solitons
Summary
We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw–Rebbi (JR) models. We show that the cooperation of time-reversal, charge-conjugation, parity, and discrete field rotation ( Zn ) symmetries protects and identifies the various types of soliton states via bulk-boundary correspondence. The JR model shows charge-conjugate and parity-invariant solitons (equivalently, nonchiral solitons) in the presence of Z2 field rotation symmetry, otherwise it shows chiral solitons with broken C and P symmetries.
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