The exact elementary excitations in a typical U(1) symmetry broken quantum
integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor,
next nearest neighbor and chiral three spin interactions, are studied. The main
technique is that we quantify the energy spectrum of the system by the zero
roots of transfer matrix instead of the traditional Bethe roots. From the
numerical calculation and singularity analysis, we obtain the patterns of zero
roots. Based on them, we analytically obtain the ground state energy and the
elementary excitations in the thermodynamic limit. We find that the system also
exist the nearly degenerate states in the regime of $\eta\in \mathbb{R}$, where
the nearest-neighbor couplings among the z-direction are ferromagnetic. More
careful study shows that the competing of interactions can induce the gapless
low-lying excitations and quantum phase transition in the antiferromagnetic
regime with $\eta\in \mathbb{R}+i\pi$.
