Comment on "Phase separation in a two-species Bose mixture"

In an article in 2007, Mishra, Pai, and Das [Phys. Rev. A 76, 013604 (2007)] investigated the two-component Bose-Hubbard model using the numerical DMRG procedure. In the regime of inter-species repulsion $U^{ab}$ larger than the intra-species repulsion $U$, they found a transition from a uniform miscible phase to phase-separation occurring at a finite value of $U$ , e.g., at around $U=1.3$ for $\mathrm{\Delta }=U^{ab}\mathrm{/}U=1.05$ and ${\rho }_a={\rho }_b=1\mathrm{/}2$. In this comment, we show that this result is not correct and in fact the two-component Bose-Hubbard model is unstable to phase-separation for any $U^{ab}>U>0$.