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 v0,i≪1, where v0,i is the bare nesting angle at the hot spots, the temperature TKAFQCM below which Kondo coupling becomes O(1) is suppressed as logΛ/TKAFQCMlogΛ/TKFL∼gf,iv0,ilog1/v0,i, where TKFL is the Kondo temperature of the Fermi liquid with the same electronic density of states, and gf,i is the boson-impurity coupling defined at UV cutoff energy Λ. 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.