Exact solution of the Landau fixed point via bosonization

TL;DR

This paper employs bosonization to derive an exact solution for the Landau fixed point in higher-dimensional interacting spinless fermion systems, providing explicit fermion propagator calculations and insights into screening and damping phenomena.

Contribution

It presents an exact diagonalization of the bosonized Hamiltonian at the Landau fixed point, extending bosonization techniques to higher dimensions and analyzing key physical effects.

Findings

Exact fermion propagator for the Landau fixed point

Analysis of screening of long-range potentials

Discussion of Landau damping of gauge fields

Abstract

We study, via bosonization, the Landau fixed point for the problem of interacting spinless fermions near the Fermi surface in dimensions higher than one. We rederive the bosonic representation of the Fermi operator and use it to find the general form of the fermion propagator for the Landau fixed point. Using a generalized Bogoliubov transformation we diagonalize exactly the bosonized hamiltonian for the fixed point and calculate the Fermion propagator (and the quasiparticle residue) for isotropic interactions (independently of their strength). We reexamine two well known problems in this context: the screening of long range potentials and the Landau damping of gauge fields. We also discuss the origin of the Luttinger fixed point in one dimension in contrast with the Landau fixed point in higher dimensions.