  We study the XYZ spin-1/2 chain placed in a magnetic field pointing along the
x-axis. We use bosonization and a renormalization group analysis to show that
the model has a non-trivial fixed point at a certain value of the XY anisotropy
a and the magnetic field h. Hence, there is a line of critical points in the
plane (a,h) on which the system is gapless, even though the Hamiltonian has no
continuous symmetry. The quantum critical line separates a gapped commensurate
phase from a gapped incommensurate phase. Our study explains why the floating
phase of the axial next-nearest neighbor Ising (ANNNI) chain in a transverse
magnetic field is only a line, as shown by recent numerical studies.
