Abstract
We revisit an antiferromagnetic quantum phase transition with $\mathbit{Q}=2{\mathbit{k}}_{F}$, where $\mathbit{Q}$ is an ordering wave vector and ${\mathbit{k}}_{F}$ 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 an 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 $\ensuremath{\omega}/T$ scaling for antiferromagnetic quantum criticality, generally forbidden in the context of the Hertz-Moriya-Millis theory.
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