  We propose the implementation of the Holstein model by means of digital
methods in a linear chain of trapped ions. We show how the simulation fidelity
scales with the generation of phononic excitations. We propose a decomposition
and a stepwise trapped-ion implementation of the Holstein Hamiltonian. Via
numerical simulations, we study how the protocol is affected by realistic
gates. Finally, we show how measurements of the size of the simulated polaron
can be performed.
