Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential

Details Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential

2009-01-20

arxiv.org/abs/0901.3057v1

J. Phys.: Condens. Matter 21, 485501 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

REVTeX4, 8 pages, no figures

Scientific paper

10.1088/0953-8984/21/48/485501

We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We use the Bethe-Salpeter equations for the two-particle vertex in the electron-hole and the electron-electron scattering channels and derive for systems with time reversal symmetry a nonlinear integral equation the two-particle irreducible vertices from both channels must obey. We use this equation to test the existence of the diffusion pole in the two-particle vertex. We find that a singularity of the diffusion pole can exist only if it is integrable, that is only in the metallic phase in dimensions $d>2$.

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