Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions

TL;DR

This paper investigates the critical behavior of Fermi surfaces coupled to transverse gauge fields across various dimensions, revealing fixed points and scalings through a perturbative RG analysis with novel insights into higher-order corrections.

Contribution

It introduces a dimensional regularization approach to analyze critical Fermi surfaces in generic dimensions, extending previous work and uncovering the stability of fixed lines under higher-order corrections.

Findings

Existence of RG fixed lines for certain gauge theories.

Higher-order diagrams can alter the fixed point structure.

UV/IR mixing leads to one-loop exact results for some cases.

Abstract

We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields, by applying the dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of $U(1)$ and $U(1)\times U(1)$ transverse gauge couplings, and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings. Our analysis allows us to treat a critical Fermi surface of a generic dimension $m$ perturbatively in an expansion parameter $\epsilon =\left (2-m \right ) /\left (m+1 \right).$ One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain $U(1)\times U(1)$ theories, which was identified earlier for $m=1$ at one-loop order, the third-order diagrams do. However, this fixed line feature is also obtained for $m>1$, where the answer is one-loop exact due to UV/IR mixing.