Single Scale Analysis of Many Fermion Systems. Part 4: Sector Counting

TL;DR

This paper develops sector counting techniques for two-dimensional fermion systems at zero temperature, crucial for controlling renormalization group maps and analyzing particle interactions.

Contribution

It introduces a sector counting method to manage the composition of renormalization group maps in fermion systems, especially addressing particle-particle ladder irrelevance.

Findings

Sector counting controls renormalization group map composition.

Particle-particle ladders are shown to be irrelevant for asymmetric Fermi curves.

Provides tools for analyzing fermion systems at zero temperature.

Abstract

For a two dimensional, weakly coupled system of fermions at temperature zero, one principal ingredient used to control the composition of the associated renormalization group maps is the careful counting of the number of quartets of sectors that are consistent with conservation of momentum. A similar counting argument is made to show that particle-particle ladders are irrelevant in the case of an asymmetric Fermi curve.