  In this work we investigate the different states of a system of spin-1 bosons
in two potential wells connected by tunneling, with spin-dependent interaction.
The model utilizes the well-known Bose-Hubbard Hamiltonian, adding a local
interaction term that depends on the modulus of the total spin in a well,
favoring a high- or low-spin state for different signs of the coupling
constant. We employ the concept of fidelity to detect critical values of
parameters for which the ground state undergoes significant changes. The nature
of the states is investigated through evaluation of average occupation numbers
in the wells and of spin correlations. A more detailed analysis is done for a
two-particle system, but a discussion of the three-particle case and some
results for larger numbers are also presented.
