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

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.

follows the formalism of arXiv:1407.0033; have corrected a typographical error in the appendix, which led to an incorrect result for the vertex correction for the $m=1$ case; although the correction changes the RG flow equations in the main text, it does not affect our main results and conclusions; the erratum has been published in Phys. Rev. Research 5, 039001 (2023)

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