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Phys Rev Lett. 2013 Dec 6;111(23):230404. Epub 2013 Dec 6.

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

Author information

1
Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid E-28006, Spain and Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
2
Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid E-28006, Spain and Facultad de Matemáticas, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid E-28040, Spain.
3
Facultad de Matemáticas, Universidad Complutense de Madrid, Avenida Complutense s/n, Madrid E-28040, Spain.
4
Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid E-28006, Spain.

Abstract

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 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.

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