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

TL;DR

This paper critically compares numerical and analytical results on electron-phonon interactions in the Hubbard model, linking the observed vertex function behavior to phase separation tendencies at high temperatures.

Contribution

It provides an analytical perspective on numerical findings, connecting the electron-phonon vertex upturn to phase separation instability in the Hubbard model.

Findings

Analytical results align with numerical data for large U.

Upturn of the electron-phonon vertex linked to phase separation.

Phase separation tendency occurs at high temperatures.

Abstract

In cond-mat/0306131 Huang {\em 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.