  Frustrated quantum magnets are a central theme in condensed matter physics
due to the richness of their phase diagrams. They support a panoply of phases
including various ordered states and topological phases. Yet, this problem has
defied a solution for a long time due to the lack of controlled approximations
which make it difficult to distinguish between competing phases. Here we report
the discovery of a special quantum macroscopically degenerate point in the XXZ
model on the spin-1/2 kagome quantum antiferromagnet for the ratio of Ising to
antiferromagnetic transverse coupling Jz/J=-1/2. This point is proximate to
many competing phases explaining the source of the complexity of the phase
diagram. We identify five phases near this point including both spin-liquid and
broken-symmetry phases and give evidence that the kagome Heisenberg
antiferromagnet is close to a transition between two phases.
