Comment on ``Electron-phonon Vertex in the Two-dimensional One-band Hubbard Model''

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In cond-mat/0306131 Huang et al. reported for the first time a numerical evidence for the predominance of small phonon momenta in the electron-phonon coupling induced by electronic correlation. They report also an upturn of the electron-phonon vertex function for small momenta as function of the Hubbard repulsion U for sufficient large U. In this comment we compare their Quantum Monte Carlo data with analytical results based on slave-boson techniques for generic U. We associate the upturn of the electron-phonon vertex function with the tendency towards a phase separation instability at large temperatures.