  When skyrmions representing nucleons are put on crystal lattice and
compressed to simulate high density, there is a transition above the normal
nuclear matter density $n_0$ from a matter consisting of skyrmions with integer
baryon charge to a state of half-skyrmions with half-integer baryon charge. We
exploit this observation in an effective field theory formalism to access dense
baryonic system. We find that the topology change involved implies a changeover
from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate
in the nucleon "melted off." The $\sim 80%$ of the nucleon mass that remains,
invariant under chiral transformation, points to the origin of the (bulk of)
proton mass that is not encoded in the standard mechanism of spontaneously
broken chiral symmetry. The topology change engenders a drastic modification of
the nuclear tensor forces, thereby nontrivially affecting the EoS, in
particular, the symmetry energy, for compact star matter. It brings in
stiffening of the EoS needed to accommodate a neutron star of $\sim 2$ solar
mass. The strong effect on the EoS in general and in the tensor force structure
in particular will also have impact on processes that could be measured at
RIB-type accelerators.
