On the Impossibility of Electronic Phase Separation in the $D=1,2$ Dimensional Hubbard Model at T=0

We show explicitly that the one- and two-dimensional Hubbard model does not show phase separation at any filling at T=0. Apart from a single plausible assumption, only known exact results and symmetry properties for the one-band Hubbard model are used. Implications for usage of the simple one-band Hubbard model for analysing the physics of cuprate superconductors are discussed. We also discuss models where electronic phase separation might generically occur, in the specific context of colossal magneto-resistance manganites.