  We study an organic Hydrogen bonded material $\rm{H_2SQ}$ analytically and
map out the phase diagram as well as low energy excitations in the relevant
parameter space. At zeroth order the dynamics is governed by plaquette
interaction (product of $\sigma_z$ over a plaquette) which defines a $Z_2$
gauge theory and a deconfinement phase satisfying "ice rules". The system is
studied under additional interactions such as an external Zeeman field (with
strength $K$) in $x$-direction, a inter-molecular interaction (with strength
$J_1$) and a dipole-dipole interaction with strength $J_2$ such that
$K>J_1>J_2$. The effect of dipole-dipole interaction removes the local $Z_2$
symmetry and gives rise to four global degenerate states with Ferroeletric
order. Using meanfield analysis we chart out the phase diagram for classical
version of the model and find $K_c$ which defines the transition from
disordered phase to ordered phase in $J_1, K$ plane for various values of
$J_2$. We find that presence of $J_1$ and $J_2$ tends to stabilize the
deconfined phases. Over the classical ground states we perform spin-wave
analysis and surprisingly find that quantum fluctuations does not remove the
classical degeneracy at all at quadratic level. The spin-wave spectrum is found
for the four global degenerate ground states which shows both gapped spectrum
and gapless spectrum (near the vicinity of CDT transition) for $J_2=0$. However
for $J_2$ finite, the spectrum is always gapped. We perform PCUT analysis to
improve the results of spin-wave analysis and calculate ground state energy and
one particle dispersion and gap at high symmetry point. Using this we draw the
phase boundary between confined and deconfined phase in the $K-J_1$ plane. The
effect of $J_2$ is also discussed in the resulting phase boundary.
