  A novel Bethe ansatz scheme is proposed to investigate the exact physical
properties of an integrable anisotropic quantum spin chain with competing
interactions among the nearest, next nearest neighbor and chiral three spin
couplings, where the boundary condition is the twisted one. The eigenvalue of
the transfer matrix is characterized by its zero roots instead of the
traditional Bethe roots. Based on the exact solution, the conserved momentum
and charge operators of this U(1)-symmetry broken system are obtained. The
ground state energy and density of rapidities are calculated. It is found that
there exist three kinds of elementary excitations and the corresponding
dispersion relations are obtained, which gives a different picture from that
with periodic boundary condition.
