The renormalization group for interacting fermions: from Fermi liquids to quantum dots

TL;DR

This paper applies the renormalization group approach to Fermi liquids and quantum dots, demonstrating fixed points and analyzing strong coupling phases with large N and Random Matrix techniques.

Contribution

It extends the renormalization group framework to ballistic quantum dots and explores fixed points and strong coupling phases using advanced methods.

Findings

Landau theory is a fixed point for clean Fermi liquids

Universal Hamiltonian is a fixed point for weakly coupled quantum dots

Strong coupling phase analyzed with large N and Random Matrix methods

Abstract

The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal Hamiltonian is shown to be a fixed point for weak coupling. The strong coupling phase is analyzed using large N and Random Matrix methods.