Year: 2006
Type: article
Abstract: We show that in two dimensions (2D) a systematic expansion of the self-energy and the effective interaction of a dilute electron gas in powers of the two-body $T$ matrix ${T}_{0}$ can be generated from an exact hierarchy of the functional renormalization group equations for 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.
Source: Physical Review B
Authors: Francesca Sauli, Peter Kopietz
Institution: Goethe University Frankfurt
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2073650286