Fermi Systems with Strong Forward Scattering

TL;DR

This paper reviews the theory of interacting Fermi systems dominated by forward scattering, covering Fermi liquids and non-Fermi liquid phases, analyzing critical dimensions, and discussing low-energy behaviors and conservation laws.

Contribution

It provides a comprehensive review of forward scattering in Fermi systems, including non-perturbative methods and the role of conservation laws in low-energy effective theories.

Findings

Identification of critical dimensions for different universality classes

Analysis of the behavior of the momentum distribution and response functions

Demonstration of non-perturbative treatment techniques for forward scattering

Abstract

We review the theory of interacting Fermi systems whose low-energy physics is governed by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different "universality classes", and discuss the behavior of physical quantities as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective low-energy theories. Particular attention is payed to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.