  Recent experimental progress in magnetic atoms and polar molecules has
created the prospect of simulating dipolar Hubbard models with off-site
interactions. When applied to real-space cylindrical optical lattices, these
anisotropic dipole-dipole interactions acquire a tunable spatially-dependent
component while they remain translationally-invariant in the axial direction,
creating a sublattice structure in the azimuthal direction. We numerically
study how the coexistence of these classes of interactions affects the ground
state of hardcore dipolar bosons at half-filling in a finite-size cylindrical
optical lattice with octagonal rings. When these two interaction classes
cooperate, we find a solid state where the density order is determined by the
azimuthal sublattice structure and builds smoothly as the interaction strength
increases. For dipole polarisations where the axial interactions are
sufficiently repulsive, the repulsion competes with the sublattice structure,
significantly increasing entanglement and creating two distinct ordered density
patterns. The spatially-varying interactions cause the emergence of these
ordered states in small lattices as a function of interaction strength to be
staggered according to the azimuthal sublattices.
