  Coulomb spin liquids are topological magnetic states obeying an emergent
Gauss' law. Little distinction has been made between different kinds of Coulomb
liquids. Here we show how a series of distinct Coulomb liquids can be generated
straightforwardly by varying the constraints on a classical spin system. This
leads to pair creation/annihilation, and coalescence, of topological defects of
an underlying vector field. The latter makes higher-rank spin liquids, of
recent interest in the context of fracton theories, with attendant multi-fold
pinch points in the structure factor, appear naturally. New Coulomb liquids
with an abundance of pinch points also arise. We thus establish a new and
general route to uncovering exotic Coulomb liquids, via the manipulation of
topological defects in momentum space.
