Abstract. We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We analyze Bethe–Salpeter equations for the two-particle vertex in the electron–hole and the electron–electron scattering channels and derive for systems with electron–hole symmetry a nonlinear integral equation that the two-particle irreducible vertices from both channels must obey. We use this equation and a parquet decomposition of the full vertex to set restrictions on an admissible form of the two-particle singularity induced by probability conservation. We find that such a singularity in two-particle functions can exist only if it is integrable, that is, only in the metallic phase in dimensions d>2.

Print publication: Issue 48 (2 December 2009)
Received 21 July 2009, in final form 19 October 2009
Published 6 November 2009