  We study a quantum spin system on a honeycomb lattice, when it includes
frustration and distortion in antiferromagnetic (AF) exchange interactions. We
transform the spin system onto a nonlinear sigma model (NLSM) in a new way
preserving the original spin degrees of freedom. Assisted by a renormalization-
group argument, the NLSM provides a ground-state phase diagram consisting of an
ordered AF phase and a disordered spin-gap phase.
  The spin-gap phase extends from a strong frustration regime to a strong
distortion regime, showing that the disordered ground states are essentially
the same in both the regimes. In the spin-half case, the spin-gap phase for the
spin system on a honeycomb lattice is larger than that for the J1-J2 model on a
square lattice.
