  The relationship between classical and quantum mechanics is usually
understood via the limit $\hbar \rightarrow 0$. This is the underlying idea
behind the quantization of classical objects. The apparent incompatibility of
general relativity with quantum mechanics and quantum field theory has
challenged for many decades this basic idea. We recently showed the emergence
of classical dynamics for very general quantum lattice systems with mean-field
interactions, without (complete) supression of its quantum features, in the
infinite volume limit. This leads to a theoretical framework in which the
classical and quantum worlds are entangled. Such an entanglement is noteworthy
and is a consequence of the highly non-local character of mean-field
interactions. Therefore, this phenomenon should not be restricted to systems
with mean-field interactions only, but should also appear in presence of
interactions that are sufficiently long-range, yielding effective, classical
background fields, in the spirit of the Higgs mechanism of quantum field
theory. In order to present the result in a less abstract way than in its
original version, here we apply it to a concrete, physically relevant, example
and discuss, by this means, various important aspects of our general approach.
The model we consider is not exactly solvable and the particular results
obtained are new.
