Scaling approach to itinerant quantum critical points

TL;DR

This paper introduces a phase space-based scaling approach to study metallic quantum critical points, allowing analysis without integrating out fermions, and applies it to a ferromagnetic transition model.

Contribution

It develops a novel scaling method for metallic quantum critical points that retains fermionic degrees of freedom and derives stability criteria for the coupled fluids.

Findings

Anomalous exponents can emerge below three dimensions.

The approach avoids integrating out fermions, simplifying analysis.

Stability criteria for conduction and spin fluids are established.

Abstract

Based on phase space arguments, we develop a simple approach to metallic quantum critical points, designed to study the problem without integrating the fermions out of the partition function. The method is applied to the spin-fermion model of a T=0 ferromagnetic transition. Stability criteria for the conduction and the spin fluids are derived by scaling at the tree level. We conclude that anomalous exponents may be generated for the fermion self-energy and the spin-spin correlation functions below $d=3$, in spite of the spin fluid being above its upper critical dimension.