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 $\Delta = U^{ab}/U = 1.05$ and $\rho_{a} = \rho_{b} = 1/2$. 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 $U^{ab} > U > 0$.
Comment: 2 pages, 3 figures, submitted to Phys. Rev. A