Kinematics of electrons near a Van Hove singularity

TL;DR

This paper analyzes electron kinematics near a Van Hove singularity in a 2D system, exploring weak coupling instabilities and comparing RG and parquet approaches to understand phase diagram properties.

Contribution

It provides a detailed comparison of RG and parquet methods in studying electron scattering near Van Hove singularities, highlighting physical process differences.

Findings

Identifies similarities and differences between RG and parquet approaches.

Discusses phase diagram properties near Van Hove singularities.

Analyzes electron scattering kinematics in detail.

Abstract

A two dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities, and it is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of the electron scattering in this model. The similitudes, and differences, between a standard Renormalization Group approach and previous work based on parquet summations of log$^2$ divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.