  We study the ground state (GS) many-body quantum entanglement of two
different transverse field models on a quasi-2D square lattice relevant to a
Hydrogen-bonded crystal, i.e, squaric acid. We measure the genuine multipartite
qubit-entanglement ($C_{\text{GME}}(\psi)$) of the ground state of very generic
models with all the possible cases of exchange couplings considered under
defect free and one lattice site defect conditions. Our results show that
creation, decay of multipartite entanglement occur for different combinations
of coupling strength. When frustration is maximum the system exhibits a peak in
concurrence after a gradual increase from disentangled state at zero field
followed by an asymptotic decay at large fields. In contrast, for a marginally
frustrated (degenerate) case though the concurrence shows a peak, the
entanglement is non-zero and large at zero fields. Our results discuss the
sensitivity of the qubit-entanglement with underlying GS of varying degree of
degeneracy. We conclude that despite of their similarities in ground state
properties, yet we see a difference in the degree of entanglement between the
two models. We conjecture this result could be due to the difference in the
amount of degeneracy and the quantum ground states of both Hamiltonians that
could dictate the results even in the thermodynamic limit.
