Causality vs. Ward identity in disordered electron systems

Abstract

We address the problem of fulfilling consistency conditions in solutions for disordered noninteracting electrons. We prove that if we assume the existence of the diffusion pole in an electron-hole symmetric theory we cannot achieve a solution with a causal self-energy that would fully fit the Ward identity. Since the self-energy must be causal, we conclude that the Ward identity is partly violated in the diffusive transport regime of disordered electrons. We explain this violation in physical terms and discuss its consequences.

4 pages, REVTeX, 6 EPS figures

References in corpus (1)

• Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation

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• Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems
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• Quantum diffusion in a random potential: A consistent perturbation theory