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that the two-hole excitation branch has a negative slope in ( µ$_{↑}$ + µ$_{↓}$ ) / 2 versus t$_{σ}$ phase diagram when t$_{σ}$ → 0 ], i.e. − (2 n$_{↑}$n$_{↓}$/U$_{↑↓}$ ) zt$_{↑}$t$_{↓}$ − ∑ $_{σ}$[ n 2 $_{σ}$/U$_{↑↓}$ − ( n 2 σ − 1) / (2 U$_{σσ}$ + U$_{↑↓}$ ) + 2 n$_{σ}$ ( n$_{σ}$ + 1) /U$_{σσ}$ ] zt 2 σ term, which occurs for the first few Mott lobes beyond a critical U$_{↑↓}$ . When this coefficient is negative, its value is most negative for the first Mott lobe , 

and therefore the effect is strongest there. However, the coef- ficient increases and eventually becomes positive as a funct ion of filling, and thus the re-entrant behavior becomes weaker a s filling increases, and it eventually disappears beyond a cri tical filling. For the parameters used in Fig. 2, this occurs only fo r the first lobe, as can be seen in the figures. We also note that the sign of this coefficient is independent of the dimensiona l- ity of the lattice, since z = 2 d enters into the coefficient only as an overall factor. 

What happens when t$_{↑}$ ̸ = t$_{↓}$ and/or U$_{↑↑}$ ̸ = U$_{↓↓}$ ? We donot expect any qualitative change for attractive interspecies inter- actions. However, for repulsive interspecies interactions, this lifts the degeneracy of the single-particle or single-hole exci- tation energies. While the transition is from a double Mott insulator to a double superfluid of both species in the degen- erate case, it is from a double-Mott insulator of both species to a Mott insulator of one species and a superfluid of the other in the nondegenerate case. 

We analyzed the zero temperature phase diagram of the two-species Bose-Hubbard (BH) model with on-site boson- boson interactions in d -dimensional hypercubic lattices, in- 

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## V. CONCLUSIONS 

