  We elucidate that the nearly phase-ordered active XY spins in contact with a
conserved, diffusing species on a substrate can be stable. For wide-ranging
model parameters, it has stable uniform phases robust against noises. These are
distinguished by generalized quasi-long range (QLRO) orientational order
logarithmically stronger or weaker than the well-known QLRO in equilibrium,
together with miniscule (i.e., hyperuniform) or giant number fluctuations,
respectively. This illustrates a direct correspondence between the two. The
scaling of both phase and density fluctuations in the stable phase-ordered
states is nonuniversal: they depend on the nonlinear dynamical couplings. For
other parameters, it has no stable uniformly ordered phase. Our model, a theory
for active spinners, provides a minimal framework for wide-ranging systems,
e.g., active superfluids on substrates, synchronization of oscillators, active
carpets of cilia and bacterial flagella and active membranes.
