  In the present work we discuss inter-species entanglement in Bose-Bose
mixtures trapped in optical lattices. This work is motivated by the observation
that, in the presence of a second component, the Mott-insulator lobe shifts
{\em{differently}} on the hole- and particle-side with respect to the Mott lobe
of the single species system (Phys. Rev. A 82, 021601, Laser Phys. 21, 1443).
We use perturbation theory, formulated in a Hilbert space decomposed by means
of lattice symmetries, in order to show that the nonuniform shift of the Mott
lobe is a consequence of an inter-species entanglement which differs in the
lowest excited states to remove and add a particle. Our results indicate that
inter-species entanglement in mixtures can provide a new perspective in
understanding quantum phase transitions. To validate our approach, we compare
our results from perturbation theory with quantum Monte Carlo simulations.
