  The generating functional of a self-interacting scalar quantum field theory
(QFT), which contains all the relevant information about real-time dynamics and
scattering experiments, can be mapped onto a collection of
multipartite-entangled two-level sensors via an interferometric protocol that
exploits a specific set of source functions. Although one typically focuses on
impulsive delta-like sources, as these give direct access to $n$-point Feynman
propagators, we show in this work that using always-on harmonic sources can
simplify substantially the sensing protocol. In a specific regime, the
effective real-time dynamics of the quantum sensors can be described by a
quantum Ising model with long-range couplings, the range and strength of which
contains all the relevant information about the renormalisation of the QFT,
which can now be extracted in the absence of multi-partite entanglement. We
present a detailed analysis of how this sensing protocol can be relevant to
characterise the long-wavelength QFT that describes quantised sound waves of
trapped-ion crystals in the vicinity of a structural phase transition, opening
a new route to characterise the associated renormalisation of sound.
