Spin-orbital correlations in the two-orbital Hubbard model

We use exact diagonalization results to investigate how the ground state of a two-site, two-orbital Hubbard model evolves in terms of the crystal field energy and a magnetic spin symmetry breaking field. We show that, based on the behavior of a properly defined composite spin-orbital correlation function, the different regions of the related phase diagrams can be classified according to the extent to which spin and orbital degrees of freedom turn out to be correlated.