Anomalous scaling of fermions and order parameter fluctuations at quantum criticality

Understand

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.