Fermions on the kink revisited

Abstract

We study fermion modes localized on the kink in the 1+1 dimensional ${\varphi }^4$ model, coupled to the Dirac fermions with backreaction. Using numerical methods we construct self-consistent solutions of the corresponding system of coupled integral-differential equations and study dependencies of the scalar field of the kink and the normalizable fermion bound states on the values of the values of the parameters of the model. We show that the backreaction of the localized fermions significantly modifies the solutions, in particular it results in spatial oscillations of the profile of the kink and violations of the reflection symmetry of the configuration.

arXiv comment14 pages, 7 figures

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Cited by in corpus (12)

• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Kinks bounded by fermions
• Fermionic spectral walls in kink collisions
• Fermion transfer in the ${\varphi }^4$ model with a half-BPS preserving impurity
• Resonance mediated by fermions in kink-antikink collisions
• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Fermions on wobbling kinks: normal versus quasinormal modes
• Scattering of fermionic isodoublets on the sine-Gordon kink
• Excited fermions on kinks and the Dirac sea
• Variational Approach to Excited Fermions on Kinks
• Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion
• Remarks on sine-Gordon kink--fermion system: localized modes and scattering