Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals

TL;DR

This paper develops a Wilsonian effective field theory for disorder-free metals near a quantum critical point, revealing new non-Fermi liquid fixed points in three dimensions where bosons and fermions are treated equally.

Contribution

It introduces a novel Wilsonian approach that treats fermions and bosons on equal footing, uncovering non-Fermi liquid fixed points absent in traditional theories.

Findings

Identifies new fixed points with Wilson-Fisher bosons coupled to non-Fermi liquids

Demonstrates the absence of superconducting instability in the large N limit

Clarifies the renormalization group flow of four-Fermi interactions

Abstract

We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm of Hertz and Millis, and treat both fermions and bosons i.e. order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high energy boson and fermion modes. Below the upper critical dimension of the theory (d=3 spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large N limit. In this limit, we find that the theory has no superconducting instability.