Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals

TL;DR

This paper investigates how critical bosonic fluctuations influence the dynamical scaling in two-dimensional metals, revealing that anomalous scaling appears at four-loop order due to subtle cancellations at lower orders.

Contribution

It demonstrates that anomalous dynamical scaling in 2D metals with critical fluctuations arises at four-loop order, extending previous understanding of the robustness of the z=3 exponent.

Findings

Anomalous dynamical scaling emerges at four-loop order.

Cancellations at three-loop order prevent anomalous contributions.

Robustness of the z=3 dynamical exponent up to three-loop order.

Abstract

We analyze the scaling theory of two-dimensional metallic electron systems in the presence of critical bosonic fluctuations with small wave vectors, which are either due to a U(1) gauge field, or generated by an Ising nematic quantum critical point. The one-loop dynamical exponent z=3 of these critical systems was shown previously to be robust up to three-loop order. We show that the cancellations preventing anomalous contributions to z at three-loop order have special reasons, such that anomalous dynamical scaling emerges at four-loop order.