Electron–phonon interaction in the strongly correlated Hubbard model

Abstract

We study numerically the renormalization of the on-site electron–phonon interaction or vertex as a function of temperature and hole doping density in the two-dimensional strongly correlated Hubbard model. In the underdoped region, we find that the forward scattering process increases monotonically with lowering temperature, whereas the backward scattering process shows little temperature dependence. With decreasing hole doping density, the electron–phonon vertex increases at small phonon momentum transfer, but decreases at large phonon momentum transfer, leading to a pronounced forward scattering peak in the small doping region. Our findings indicate that the electron–phonon interaction is strong in the high- T c superconductors and may play an important role in pairing and low-energy renormalization of quasiparticles.