Renormalization Group and Fermi Liquid Theory

TL;DR

This paper interprets Fermi liquid theory through renormalization group methods, identifying the fixed point Hamiltonian and connecting microscopic models to phenomenological descriptions, while exploring its limitations.

Contribution

It provides a Hamiltonian-based renormalization group framework for Fermi liquid theory, including corrections and extensions beyond the Fermi liquid regime.

Findings

Identified the fixed point Hamiltonian for Fermi liquids.

Showed mean field theory reproduces Landau phenomenology.

Discussed breakdown of Fermi liquid in Luttinger and Mott models.

Abstract

We give a Hamiltonian based interpretation of microscopic Fermi liquid theory within a renormalization group framework. We identify the fixed point Hamiltonian of Fermi liquid theory, with the leading order corrections, and show that this Hamiltonian in mean field theory gives the Landau phenomenological theory. A renormalized perturbation theory is developed for calculations beyond the Fermi liquid regime. We also briefly discuss the breakdown of Fermi liquid theory as it occurs in the Luttinger model, and the infinite dimensional Hubbard model at the Mott transition.