Low-density expansion for the two-dimensional electron gas

TL;DR

This paper develops a systematic low-density expansion for the two-dimensional electron gas using functional renormalization group techniques, highlighting limitations of the ladder approximation and discussing two-body scattering in various dimensions.

Contribution

It introduces a new systematic expansion method for the 2D electron gas based on the functional renormalization group, revealing the limitations of the ladder approximation.

Findings

Ladder approximation is unreliable beyond leading order in 2D.

Systematic expansion generated from exact RG hierarchy.

Singular interactions proposed by Anderson are not ruled out.

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.