Mode-mode coupling effects on dynamic spin and charge susceptibilities in high-T c superconductors

Abstract

The self-consistent and conserving approximation scheme of Kadanoff and Baym is used to derive general equations for the dynamic spin and charge susceptibilities of the 2D Hubbard hamiltonoperator. The resulting vertex corrections to the RPA susceptibilities describe coupling of a spin or charge fluctuation mode with one or two other modes. In the presence of the electronphonon interaction the vertex corrections are relatively small and thus our previous results for various physical quantities in high- T c superconductors are still valid. For the pure 2D Hubbard hamiltonoperator we calculate the averages of the dynamic susceptibilities over all wave vectors as functions of the coupling constant U/ t. The vertex corrections give rise to an enhancement of the spectral density of the charge susceptibility and to a suppression of the spectral density of the spin susceptibility. However, this effect alone is too small to yield a finite T c.