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 d(1) and d(M) mutually orthogonal directions around a few isolated points in the reciprocal space, respectively, with d(1) + d = d(M), and residing at the brink of isotropic insulation, described by N-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 epsilon = 2 - d(M) and 1/N-f, where N-f is the number of identical fermion copies (flavor number) when in conjunction d(L) = 1 When applied to three-dimensional interacting general Weyl semimetals (d(L) = 1 and d(M) = 2 ) , characterized by the Abelian monopole charge n > 1 , living at the shore of the axionic insulation (N-b = 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 d(L) = 3 and d(M) = 0 ). Consequently, emergent marginal Fermi liquids showcase only logarithmic corrections to physical observables at intermediate scales of measurements.