  We investigate the factorization, coherence and asymmetry properties of the
1d Heisenberg spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction (DMI)
and a transverse magnetic field using quantum information measures. Both
longitudinal and transverse DM vectors are considered. Using numerical DMRG, we
compute the one-tangle, two-spin concurrence and the Wigner-Yananse-skew
information. We show that a longitudinal DMI destroys the factorizability
property while a transverse DMI preserves it. We relate the absence of
factorizability to the breaking of the $U(1)$ rotation symmetry about the local
magnetization axis at each lattice site. Physically, breaking of the symmetry
manifests in the existence of a chiral current. Although the longitudinal DMI
destroys factorizability, we obtain a `pseudofactorizing' field ($h_{pf}$) at
which entanglement and hence violation of the $U(1)$ symmetry is minimal. Our
calculations indicate a phase coherent ground state at $h_{pf}$. An
entanglement transition (ET) occurs across this field which is characterized by
an enhanced but finite range of two-spin concurrence in its vicinity in
contrast with the diverging range of the concurrence for the ET across the
factorizing field ($h_{f}$). We relate the asymmetry to the `frameness' or the
ability for the state to act as a reference frame for some measurement. In
absence of longitudinal DMI (or in presence of transverse DMI), at $h_{f}$, the
single site magnetization axis specifies the common $z$-axis for the full
system but not the full Cartesian reference frame due to a lack of phase
reference. On the other hand, in the presence of a longitudinal DMI, our
results indicate that at $h_{pf}$, the local magnetization and the chiral
current are sufficient to specify the full Cartesian reference frame, with the
chiral current being the macroscopic quantity to determine the phase reference.
