Abstract

We formulate a field-theoretic description for d-dimensional interacting nodal semimetals, featuring dispersion that scales with the linear and nth power of momentum along dL and dM mutually orthogonal directions around a few isolated points in the reciprocal space, respectively, with dL+dM=d, and residing at the brink of isotropic insulation, described by Nb-component bosonic order parameter fields. The resulting renormalization group (RG) procedure, tailored to capture the associated quantum critical phenomena, is controlled by a "small"parameter ?=2-dM and 1/Nf, where Nf is the number of identical fermion copies (flavor number) when in conjunction dL=1. When applied to three-dimensional interacting general Weyl semimetals (dL=1 and dM=2), characterized by the Abelian monopole charge n>1, living at the shore of the axionic insulation (Nb=2), a leading-order RG analysis suggests the Gaussian nature of the underlying quantum phase transition, around which the critical exponents assume mean-field values. A traditional field-theoretic RG analysis yields the same outcomes for simple Weyl semimetals (n=1, dL=3, and dM=0). Consequently, emergent marginal Fermi liquids showcase only logarithmic corrections to physical observables at intermediate scales of measurements. © 2025 American Physical Society.