  Multipartite entanglement refers to the simultaneous entanglement between
multiple subsystems of a many-body quantum system. While multipartite
entanglement can be difficult to quantify analytically, it is known that it can
be witnessed through the Quantum Fisher information (QFI), a quantity that can
also be related to dynamical Kubo response functions. In this work, we first
show that the finite temperature QFI can generally be expressed in terms of a
static structure factor of the system, plus a correction that vanishes as
$T\rightarrow 0$. We argue that this implies that the static structure factor
witnesses multipartite entanglement near quantum critical points at
temperatures below a characteristic energy scale that is determined by
universal properties, up to a non-universal amplitude. Therefore, in systems
with a known static structure factor, we can deduce finite temperature scaling
of multipartite entanglement and low temperature entanglement depth without
knowledge of the full dynamical response function of the system. This is
particularly useful to study 1D quantum critical systems in which sub-power-law
divergences can dominate entanglement growth, where the conventional scaling
theory of the QFI breaks down. The 1D spin-$\frac{1}{2}$ antiferromagnetic
Heisenberg model is an important example of such a system, and we show that
multipartite entanglement in the Heisenberg chain diverges non-trivially as
$\sim \log(1/T)^{3/2}$. We verify these predictions with calculations of the
QFI using conformal field theory and matrix product state simulations. Finally
we discuss the implications of our results for experiments to probe
entanglement in quantum materials, comparing to neutron scattering data in
KCuF$_3$, a material well-described by the Heisenberg chain.
