  The transition from a gapless liquid to a gapped dimerized ground state that
occurs in the frustrated antiferromagnetic Majumdar-Ghosh (or $J_1-J_2$
Heisenberg) model is revisited from the point of view of entanglement. We study
the evolution of entanglement spectra, a "projected subspace" block entropy,
and concurrence in the Schmidt vectors through the transition. The standard
tool of Schmidt decomposition along with the existence of the unique MG point
where the ground states are degenerate and known exactly, suggests the
projection into two orthogonal subspaces that is useful even away from this
point. Of these, one is a dominant five dimensional subspace containing the
complete state at the MG point and the other contributes marginally, albeit
with increasing weight as the number of spins is increased. We find that the
marginally contributing subspace has a minimum von Neumann entropy in the
vicinity of the dimerization transition. Entanglement content between pairs of
spins in the Schmidt vectors, studied via concurrence, shows that those
belonging to the dominant five dimensional subspace display a clear progress
towards dimerization, with the concurrence vanishing on odd/even sublattices,
again in the vicinity of the dimerization, and maximizing in the even/odd
sublattices at the MG point. In contrast, study of the Schmidt vectors in the
marginally contributing subspace, as well as in the projection of the ground
state in this space, display pair concurrence which decrease on both the
sublattices as the MG point is approached. The robustness of these observations
indicate their possible usefulness in the study of models that have similar
transitions, and have hitherto been difficult to study using standard
entanglement signatures.
