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arXiv · 2512.07748

Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory

Alan Kahan·Pablo Viñas·Torsten V. Zache·Alejandro Bermudez
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Abstract

We propose and analyze a trapped-ion quantum simulator of the Jackiw-Rebbi model, a paradigmatic quantum field theory in (1+1) dimensions where solitonic excitations of a scalar field can bind fermionic zero modes leading to fractionally-charged excitations. In our approach, the scalar field is a coarse-grained description of the planar zigzag ion displacements in the vicinity of a structural phase transition. The internal electronic states of the ions encode spins with interactions mediated by the transverse phonons and in-plane spin-phonon couplings with a zigzag pattern, which together correspond to a Yukawa-coupled Dirac field. Instead of assuming a fixed soliton background, we study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system. We start by applying a Born-Oppenheimer approximation to obtain an effective Peierls-Nabarro potential for the topological kink, unveiling how the fermionic back-reaction can lead to localization of the kink. Beyond this limit, a truncated Wigner approximation combined with fermionic Gaussian states captures the quantum spreading and localization of a kink and kink-antikink scattering. Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions, predicting experimentally accessible signatures in current trapped-ion architectures.

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Alan Kahan, Pablo Viñas, Torsten V. Zache, Alejandro Bermudez. 2026-02-17. Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory. https://arxiv.org/abs/2512.07748

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