Effective Field Theory of 2D van Hove Singularities

TL;DR

This paper develops an effective field theory for 2D fermions near van Hove singularities, revealing unique divergences, UV/IR mixing, and implications for superconductivity and normal state transport, including marginal Fermi liquid behavior.

Contribution

It introduces a regularization scheme for divergences at van Hove points and explores the resulting UV/IR mixing effects on the RG flow and physical properties.

Findings

Divergences at van Hove singularities require non-standard regularization.

RG equations depend explicitly on the ratio of cut-off to bandwidth.

Normal state exhibits marginal Fermi liquid behavior.

Abstract

We study the effective field theory of 2D fermions with a short-range interaction in the presence of a van Hove singularity. We find that there are additional divergences associated with the singularity that necessitate regularization beyond the usual Wilsonian cut-off. In the full theory these divergences are cut off by the finite size of the Brillouin zone. This leads to a UV/IR mixing and causes the RG equation for the coupling constant to have an explicit dependence on the ratio of the Wilsonian cut-off to the bandwidth. We discuss the properties of the superconducting ground state and the transport properties of the normal state and show that the latter are approximately described by the marginal Fermi liquid scenario. To leading order, our results are universal in the sense that they do not depend upon the nature of the non-van Hove portion of the Fermi surface. We also comment on the van Hove scenario of high-Tc superconductivity.