Emergence of localized magnetic moments near antiferromagnetic quantum criticality

We revisit an antiferromagnetic quantum phase transition with $\bm{Q} = 2 \bm{k}_{F}$, where $\bm{Q}$ is an ordering wave vector and $\bm{k}_{F}$ is a Fermi momentum. Reformulating the Hertz-Moriya-Millis theory within the strong coupling approach to diagonalize the spin-fermion coupling term and performing the scaling analysis for an effective field theory with quantum corrections in the Eliashberg approximation, we propose a novel interacting fixed point for this antiferromagnetic quantum phase transition, where antiferromagnetic spin fluctuations become locally critical to interact with renormalized electrons. The emergence of local quantum criticality suggests a mechanism of $\omega/T$ scaling for antiferromagnetic quantum criticality, generally forbidden in the context of the Hertz-Moriya-Millis theory.