UV/IR Mixing In Non-Fermi Liquids: Higher-Loop Corrections In Different Energy Ranges

TL;DR

This paper investigates higher-loop quantum corrections at the Ising-nematic critical point with a Fermi surface, revealing that for a 2D Fermi surface, one-loop results remain exact across multiple energy regimes.

Contribution

It applies a dimensional regularization scheme to analyze higher-loop corrections, demonstrating the persistence of one-loop exactness in specific cases.

Findings

Higher-loop diagrams contribute in the intermediate energy range.

For m=2, one-loop results are exact in both infrared and intermediate regimes.

Dimensional regularization effectively captures the crossover behavior.

Abstract

We revisit the Ising-nematic quantum critical point with an $m$-dimensional Fermi surface by applying a dimensional regularization scheme, introduced in Phys. Rev. B 92, 035141 (2015). We compute the contribution from two-loop and three-loop diagrams in the intermediate energy range controlled by a crossover scale. We find that for $m=2 $, the corrections continue to be one-loop exact for both the infrared and intermediate energy regimes.