Exploring Spin-Holstein and Spin-Frohlich models with Trapped Ions

Electron-phonon interactions are responsible for several emergent phenomena in solids and the condensed phase, including superconductivity, charge density waves, and energy transfer. The Holstein and Frohlich models are commonly used to describe the interaction between fermions (mappable to spin-½ systems) and local bosonic excitations in materials, depending on the range of their interactions. However, studying these systems exactly is challenging in the intermediate regime where there is no clear separation of timescales between phonon and electron dynamics, limiting the accessible system size with numerical methods. Trapped ions are a promising platform for exploring spin-boson models and spin-spin interactions in a scalable manner, particularly in the challenging intermediate regime [1,2,3]. We theoretically investigate Spin-Holstein and Frohlich models in the context of multi-ion crystals, using tunable long-range spin hopping and spin-phonon interactions with multiple modes . We study the dynamics of single-spin excitations and the formation of polarons through the excitation-transport rate, the effective polaronic mass, electron-phonon correlations, and spectral functions. We propose a trapped-ion experimental setting to realize such models using locally addressed laser beams for coherent manipulation, and discuss techniques to measure spin, phonon displacement, spin-spin, and spin-phonon observables.

[1] V. So et al. , Sci. Adv.10,eads8011 (2024).

[2] D. Fallas Padilla et al. , PRX Quantum 6, 040301 (2025).

[3] J. Knorzer, et al. Phys. Rev. Lett. 128, 120404 (2022)