  Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a
systematic framework to investigate the competition between emergent phases in
frustrated two-dimensional XY quantum magnets. Application of the method to the
antiferromagnetic honeycomb spin-1/2 $J_1$-$J_2$ XY model reveals an
unconventional phase transition between two Chern-Simons orders: the
Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions.
We show that in the spin language, this transition translates to the transition
from the planar N\'{e}el state to the non-uniform chiral spin-liquid that was
proposed earlier in the literature. Namely, the Chern-Simons superconductor
describes the planar N\'{e}el state, while the Chern-Simons exciton insulator
corresponds to the non-uniform chiral spin-liquid. These results are further
confirmed by our high-precision tensor network calculation, which provides the
first numerical evidence for the transition from N\'{e}el order to a
non-uniform chiral spin-liquid. We argue that the developed method can be
applied to other frustrated quantum magnets of XXZ type and can detect
unconventional phase transitions.
