  In this study, a spin-1/2 extended anisotropic XY chain has been introduced
in which both time reversal and SU(2) symmetries are broken but $Z_2$ symmetry
is preserved. Magnetic and topological phase diagrams in the parameter space
have been drawn in the presence of transverse magnetic field. Entanglement
measures like mutual information and quantum discord are also evaluated and it
indicates that these transitions are second order in nature. Quantum phase
transition is noted at zero magnetic field, as well as magnetic long range
order is found to withstand magnetic field of any strength. Exact analytic
results for spin-spin correlation functions have been obtained in terms of
Jordan Wigner fermionization. Existence of long range magnetic order has been
investigated numerically by finding correlation functions as well as the Binder
cumulant in the ground state. Dispersion relation, ground state energy, and
energy gap are obtained analytically. In order to find the topologically
nontrivial phase, sign of Pfaffian invariant and value of winding number have
been evaluated. Both magnetic and topological phases are robust against the
magnetic field and found to move coercively in the parameter space with the
variation of its strength. Long range orders along two orthogonal directions
and two different topological phases are found and their one-to-one
correspondence has been found. Finally casting the spinless fermions onto
Majorana fermions, properties of zero energy edge states are studied. Three
different kinds of Majorana pairings are noted. In the trivial phase,
next-nearest-neighbor Majorana pairing is found, whereas two different types of
nearest-neighbor Majorana pairings are identified in the topological
superconducting phase.
