  Incompressibility plays a key role in the geometric description of fractional
quantum Hall fluids. It is naturally related to quantum area-preserving
diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which
gives rise to an emergent non-relativistic massive spin-2 mode propagating in
the bulk. The corresponding metric tensor can be identified with a nematic
order parameter for the bulk states. In the linearised regime with a flat
background, it has been shown that this mode can be described by a spin-2
Schroedinger action. However, quantum area-preserving diffeomorphisms also
suggest the existence of higher-spin modes that cannot be described through
nematic fractional quantum Hall states. Here, we consider p-atic Hall phases,
in which the corresponding p-atic order parameters are related to higher-rank
symmetric tensors. We then show that in this framework, non-relativistic
massive chiral higher-spin fields naturally emerge and that their dynamics is
described by higher-spin Schroedinger actions. We finally show that these
effective actions can be derived from relativistic massive higher-spin theories
in 2+1 dimensions after taking a non-relativistic limit.
