  We report a combined analytical and density matrix renormalized group study
of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform
Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The
numerically determined phase diagram of this model, which features two ordered
Ising phases and a critical Luttinger liquid one with fully broken
spin-rotational symmetry, agrees well with the predictions of Garate and
Affleck [Phys. Rev. B 81, 144419 (2010)]. We also confirm the prevalence of the
N z N\'eel Ising order in the regime of comparable DM and magnetic field
magnitudes.
