We analyze Bethe-Salpeter equations for the two-particle vertex in the electron-electron and electron-hole channels and demonstrate that the low-energy singularity in two-particle functions (diffusion pole) can exist only if it is integrable. Consequently, there is no such a singularity in the localized phase.
We analyze Bethe-Salpeter equations for the two-particle vertex in the electron-electron and electron-hole channels and demonstrate that the low-energy singularity in two-particle functions (diffusion pole) can exist only if it is integrable. Consequently, there is no such a singularity in the localized phase. (en)