  Fracton phases are a particularly exotic type of quantum spin liquids where
the elementary quasiparticles are intrinsically immobile. These phases may be
described by unconventional gauge theories known as tensor or multipolar gauge
theories, characteristic for so-called type-I or type-II fracton phases,
respectively. Both variants have been associated with distinctive singular
patterns in the spin structure factor, such as multifold pinch points for
type-I and quadratic pinch points for type-II fracton phases. Here, we assess
the impact of quantum fluctuations on these patterns by numerically
investigating the spin $S=1/2$ quantum version of a classical spin model on the
octahedral lattice featuring exact realizations of multifold and quadratic
pinch points, as well as an unusual pinch line singularity. Based on large
scale pseudo fermion and pseudo Majorana functional renormalization group
calculations, we take the intactness of these spectroscopic signatures as a
measure for the stability of the corresponding fracton phases. We find that in
all three cases, quantum fluctuations significantly modify the shape of pinch
points or lines by smearing them out and shifting signal away from the
singularities in contrast to effects of pure thermal fluctuations. This
indicates possible fragility of these phases and allows us to identify
characteristic fingerprints of their remnants.
