Local quantum criticality at the nematic quantum phase transition

We discuss the finite temperature properties of the fermion correlation function near the fixed-point theory of the charge 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 ultralocal behavior in space, while the low-frequency behavior of the equal-position autocorrelation 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.