Ultraviolet/infrared mixing-driven suppression of Kondo screening in the antiferromagnetic quantum critical metal

We study a magnetic impurity placed in the two-dimensional antiferromagnetic quantum critical metal (AFQCM), using the field-theoretic functional renormalization group. Critical spin fluctuations represented by a bosonic field compete with itinerant electrons to couple with the impurity through the spin-spin interaction. At long distances, the antiferromagnetic electron-impurity (Kondo) coupling dominates over the boson-impurity coupling. However, the Kondo screening is weakened by the boson with increasing severity as the hot spots connected by the magnetic ordering wave vector are better nested. For ${v}_{0,i}\ensuremath{\ll}1$, where ${v}_{0,i}$ is the bare nesting angle at the hot spots, the temperature ${T}_{K}^{\mathrm{AFQCM}}$ below which Kondo coupling becomes $O(1)$ is suppressed as $\frac{log\mathrm{\ensuremath{\Lambda}}/{T}_{K}^{\mathrm{AFQCM}}}{log\mathrm{\ensuremath{\Lambda}}/{T}_{K}^{\mathrm{FL}}}\ensuremath{\sim}\frac{{g}_{f,i}}{{v}_{0,i}log1/{v}_{0,i}}$, where ${T}_{K}^{\mathrm{FL}}$ is the Kondo temperature of the Fermi liquid with the same electronic density of states, and ${g}_{f,i}$ is the boson-impurity coupling defined at UV cutoff energy $\mathrm{\ensuremath{\Lambda}}$. The remarkable efficiency of the single collective field in hampering the screening of the impurity spin by the Fermi surface originates from ultraviolet/infrared (UV/IR) mixing: bosons with momenta up to a UV cutoff actively suppress Kondo screening at low energies.