Wilsonian effective field theory of 2D van Hove singularities

TL;DR

This paper develops a Wilsonian effective field theory for 2D fermions with van Hove singularities, revealing multiple marginal interactions, a scale-dependent RG flow, and confirming the robustness of the marginal Fermi liquid scenario.

Contribution

It introduces a renormalizable effective field theory framework for 2D fermions near van Hove singularities, highlighting multiple marginal interactions and a scale-dependent RG flow.

Findings

Multiple marginal interactions with nontrivial RG flow.

The Cooper instability is strongest in the BCS channel.

The marginal Fermi liquid scenario is robust near van Hove singularities.

Abstract

We study 2D fermions with a short-range interaction in the presence of a van Hove singularity. It is shown that this system can be consistently described by an effective field theory whose Fermi surface is subdivided into regions as defined by a factorization scale, and that the theory is renormalizable in the sense that all of the counterterms are well defined in the IR limit. The theory has the unusual feature that the renormalization group equation for the coupling has an explicit dependence on the renormalization scale, much as in theories of Wilson lines. In contrast to the case of a round Fermi surface, there are multiple marginal interactions with nontrivial RG flow. The Cooper instability remains strongest in the BCS channel. We also show that the marginal Fermi liquid scenario for the quasiparticle width is a robust consequence of the van Hove singularity. Our results are universal in the sense that they do not depend on the detailed properties of the Fermi surface away from the singularity.