title: Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential.
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.
authors.affiliation: Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Praha, Czech Republic.
authors.forename: V
authors.initials: V
authors.lastname: Janiš