  Recent experimental observation of weak ergodicity breaking in Rydberg atom
quantum simulators has sparked interest in quantum many-body scars -
eigenstates which evade thermalisation at finite energy densities due to novel
mechanisms that do not rely on integrability or protection by a global
symmetry. A salient feature of some quantum many-body scars is their sub-volume
bipartite entanglement entropy. In this work we demonstrate that such exact
many-body scars also possess extensive multipartite entanglement structure if
they stem from an su(2) spectrum generating algebra. We show this analytically,
through scaling of the quantum Fisher information, which is found to be
super-extensive for exact scarred eigenstates in contrast to generic thermal
states. Furthermore, we numerically study signatures of multipartite
entanglement in the PXP model of Rydberg atoms, showing that extensive quantum
Fisher information density can be generated dynamically by performing a global
quench experiment. Our results identify a rich multipartite correlation
structure of scarred states with significant potential as a resource in quantum
enhanced metrology.
