Low-density expansion for the two-dimensional electron gas
Abstract
We show that in two dimensions (2D) a systematic expansion of the self-energy and the effective interaction of the dilute electron gas in powers of the two-body T-matrix T_0 can be generated from the exact hierarchy of functional renormalization group equations for the one-particle irreducible vertices using the chemical potential as flow parameter. Due to the interference of particle-particle and particle-hole channels at order T_0^2, in 2D the ladder approximation for the self-energy is not reliable beyond the leading order in T_0. We also discuss two-body scattering in vacuum in arbitrary dimensions from the renormalization group point of view and argue that the singular interaction proposed by Anderson [Phys. Rev. Lett. 65, 2306 (1990)] cannot be ruled out on the basis of the ladder approximation.
Cite
@article{arxiv.cond-mat/0608423,
title = {Low-density expansion for the two-dimensional electron gas},
author = {Francesca Sauli and Peter Kopietz},
journal= {arXiv preprint arXiv:cond-mat/0608423},
year = {2007}
}
Comments
4 pages, 1 figure, typos corrected