Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

TL;DR

This paper explores the analytical solutions and dualities of fermion-soliton configurations in a modified Toda model, revealing Majorana zero modes, bound states, and non-perturbative effects with potential applications in physics and quantum computation.

Contribution

It uncovers fermion-soliton dualities, analytical zero and bound states, and the impact of fermion back-reaction in a coupled Toda-fermion model, introducing novel models and charge relations.

Findings

Analytical zero modes, in-gap states, and BIC in the model.

Fermion-soliton duality mappings between weak and strong coupling.

Zero mode catalyzes the emergence of a new kink with lower topological charge.

Abstract

A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the continuum (BIC) for topological configurations of the scalar field. Fermion-soliton duality mappings are uncovered for the bound state spectrum, which interpolates the weak and strong coupling sectors of the model and give rise to novel Thirring-like and multi-frequency sine-Gordon models, respectively. The non-perturbative effects of the back-reaction of the fermion bound states on the kink are studied and it is shown that the zero mode would catalyze the emergence of a new kink with lower topological charge and greater slope at the center, in the strong coupling limit of the model. For special topological charges and certain relative phases of the fermion components the kinks can host Majorana zero modes. The Noether, topological and a novel nonlocal charge densities satisfy a formula of the Atiyah-Patodi-Singer-type. Our results may find applications in several branches of non-linear physics, such as confinement in QCD$_2$, braneworld models, high $T_c$ superconductivity and topological quantum computation. We back up our results with numerical simulations for continuous families of topological sectors.