Anomalous scaling of fermions and order parameter fluctuations at quantum criticality

TL;DR

This paper investigates the quantum critical point between a semimetal and a superfluid in a fermionic system, revealing anomalous scaling and non-Fermi liquid behavior due to coupled fermion-boson interactions.

Contribution

It develops a coupled renormalization group framework to analyze quantum criticality beyond the Hertz-Millis approach, capturing anomalous scaling in fermions and order parameter fluctuations.

Findings

Fermions and bosons exhibit anomalous scaling at the critical point.

The model shows non-Fermi liquid behavior near quantum criticality.

Order parameter fluctuations are non-Gaussian at the transition.

Abstract

We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis approach since integrating out the fermions leads to a singular Landau-Ginzburg order parameter functional. We therefore derive and solve coupled renormalization group equations for the fermionic degrees of freedom and the bosonic order parameter fluctuations. In two spatial dimensions, fermions and bosons acquire anomalous scaling dimensions at the quantum critical point, associated with non-Fermi liquid behavior and non-Gaussian order parameter fluctuations.