2006/08/31 by Francesca Sauli, Peter Kopietz · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Electron #Fermi gas #Hierarchy #Mathematical physics #Order (exchange) #Particle density #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Renormalization #Renormalization group #Self-energy #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.74.193106
published as Phys. Rev. B 74, 193106 (2006) · 4 pages, 1 figure, typos corrected
openalex publication_date 2006/11/17 · arxiv created 2006/11/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 T0 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 T02, in 2D the ladder approximation for the self-energy is not reliable beyond the leading order in T0. 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.