Conserving approximations for response functions of the Fermi gas in a random potential
Institute of Physics, The Czech Academy of Sciences, Na Slovance 2, 18221
Praha 8, Czech Republic
Received in final form: 12 May 2016
Published online: 20 July 2016
One- and two-electron Green functions are simultaneously needed to determine the response functions of the electron gas in a random potential. Reliable approximations must retain consistency between the two types of Green functions expressed via Ward identities so that their output is compliant with macroscopic symmetries and conservation laws. Such a consistency is not directly guaranteed when summing nonlocal corrections to the local (dynamical) mean field. We analyze the reasons for this failure and show how the full Ward identity can generically be implemented in the diagrammatic approach to the vertex functions without breaking the analytic properties of the self-energy. We use the low-energy asymptotics of the conserving two-particle vertex determining the singular part of response and correlation functions to derive an exact representation of the diffusion constant in terms of Green functions of the perturbation theory. We then calculate explicitly the leading vertex corrections to the mean-field diffusion constant due to maximally-crossed diagrams.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016