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

TL;DR

This paper derives Lieb-Robinson bounds for spin-boson lattice models, applies them to trapped ion systems, and suggests experimental tests to observe potentially faster spin correlation propagation than previously known.

Contribution

It introduces a new Lieb-Robinson bound for spin-boson models and applies it to trapped ions, revealing faster correlation propagation possibilities.

Findings

Propagation of spin correlations can be faster than current experimental regimes.

Proposed measurement scheme via crystal fluorescence to test the bounds.

Lieb-Robinson bounds hold for spin-boson lattice models.

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 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.