`Local' Quantum Criticality at the Nematic Quantum Phase Transition

TL;DR

This paper analyzes the finite temperature behavior of fermion correlations near the nematic quantum critical point in metals, revealing universal scaling and ultra local spatial correlations despite being above the upper critical dimension.

Contribution

It demonstrates that the equal-time fermion correlation function exhibits universal scaling and ultra local behavior at the nematic QCP, extending understanding of quantum criticality in metallic systems.

Findings

Equal-time fermion correlation function shows universal scaling near QCP

Correlation function is ultra local in space in the quantum critical regime

Low-frequency auto correlation behaves like a Fermi liquid

Abstract

We discuss the finite temperature properties of the fermion correlation function near the fixed point theory of the nematic quantum critical point (QCP) of a metallic Fermi system. We show that though the fixed point theory is above its upper critical dimension, the equal time fermion correlation function takes on a universal scaling form in the vicinity of the QCP. We find that in the quantum critical regime, this equal-time correlation function has an ultra local behavior in space, while the low-frequency behavior of the equal-position auto correlation function is that of a Fermi liquid up to subdominant terms. This behavior should also apply to other quantum phase transitions of metallic Fermi systems.