1. Symmetry-protected solitons and bulk-boundary correspondence in generalized Jackiw–Rebbi models
- Author
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Sang Hoon Han, Chang-geun Oh, and Sangmo Cheon
- Subjects
Physics ,Multidisciplinary ,Fermionic field ,Field (physics) ,Science ,Degenerate energy levels ,Parity (physics) ,Fermion ,Symmetry (physics) ,Article ,Topological defects ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Homogeneous space ,symbols ,Medicine ,Soliton ,Theoretical physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematical physics ,Topological matter - 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 ($$Z_n$$ 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 $$Z_2$$ Z 2 rotation symmetry, whereas it shows chiral solitons with the broken $$Z_2$$ Z 2 rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only $$Z_2$$ Z 2 rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced $$Z_4$$ 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.
- Published
- 2021