Lieb-Robinson bounds for spin-boson lattice models and trapped ions

J. Juenemann, A. Cadarso, D. Perez-Garcia, A. Bermudez, J.J. Garcia-Ripoll

We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins 
interacting through a bosonic lattice field, which satisfies itself a Lieb-Robinson bound in the 
absence of spin-boson couplings. We apply these bounds to a system of trapped ions, and find that 
the propagation of spin correlations, as mediated by the phonons of the ion crystal, can be faster 
than the regimes currently explored in experiments. We propose a scheme to test the bounds by 
measuring retarded correlation functions via the crystal fluorescence. 

Phys. Rev. Lett. 111, 230404 (2013)