  We report all phases and corresponding critical lines of the quantum
anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction
along with uniform and alternating transverse magnetic fields (ATXY) by using
appropriately chosen order parameters. We prove that when DM interaction is
weaker than the anisotropy parameter, it has no effect at all on the
zero-temperature states of the XY model with uniform transverse magnetic field
which is not the case for the ATXY model. However, when DM interaction is
stronger than the anisotropy parameter, we show appearance of a new gapless
phase - a chiral phase - in the XY model with uniform as well as alternating
field. We further report that first derivatives of nearest neighbor two-site
entanglement with respect to magnetic fields can detect all the critical lines
present in the system. We also observe that the factorization surface at
zero-temperature present in this model without DM interaction becomes a volume
on the introduction of the later. We find that DM interaction can generate
bipartite entanglement sustainable at large times, leading to a proof of
ergodic nature of bipartite entanglement in this system, and can induce a
transition from non-monotonicity of entanglement with temperature to a
monotonic one.
