  We investigate whether the many-body ground states of bosons in a generalized
two-mode model with localized inhomogeneous single-particle orbitals and
anisotropic long-range interactions (e.g. dipole-dipole interactions), are
coherent or fragmented. It is demonstrated that fragmentation can take place in
a single trap for positive values of the interaction couplings, implying that
the system is potentially stable. Furthermore, the degree of fragmentation is
shown to be insensitive to small perturbations on the single-particle level.
