  We theoretically consider ultracold polar molecules in a wave guide. The
particles are bosons, they experience a periodic potential due to an optical
lattice oriented along the wave guide and are polarised by an electric field
orthogonal to the guide axis. The array is mechanically unstable by opening the
transverse confinement in the direction orthogonal to the polarizing electric
field and can undergo a transition to a double-chain (zigzag) structure. For
this geometry we derive a multi-mode generalized Bose-Hubbard model for
determining the quantum phases of the gas at the mechanical instability taking
into account the quantum fluctuations in all directions of space. Our model
limits the dimension of the numerically relevant Hilbert subspace by means of
an appropriate decomposition of the field operator, which is obtained from a
field theoretical model of the linear-zigzag instability. We determine the
phase diagrams of small systems using exact diagonalization and find that, even
for tight transverse confinement, the aspect ratio between the two transverse
trap frequencies controls not only the classical but also the quantum
properties of the ground state in a non-trivial way. Convergence tests at the
linear-zigzag instability demonstrate that our multi-mode generalized
Bose-Hubbard model can catch the essential features of the quantum phases of
dipolar gases in confined geometries with a limited computational effort.
