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

TL;DR

This paper investigates how critical spin fluctuations in a 2D antiferromagnetic quantum critical metal suppress Kondo screening of a magnetic impurity, revealing UV/IR mixing effects that weaken impurity screening at low temperatures.

Contribution

It introduces a field-theoretic renormalization group analysis showing UV/IR mixing causes suppression of Kondo screening in AFQCM, a novel insight into impurity behavior in quantum critical metals.

Findings

Kondo screening is weakened by bosonic fluctuations as hot spots are better nested.

The Kondo temperature is suppressed logarithmically by UV/IR mixing effects.

Single collective bosonic field hampers impurity screening more efficiently than previously understood.

Abstract

We study a magnetic impurity immersed 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 an increasing severity as the hot spots connected by the magnetic ordering wave-vector are better nested. For $v_{0,i} \ll 1$, 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 $\frac{\log \Lambda/T_K^{\mathrm{AFQCM}}}{\log \Lambda/T_K^{\mathrm{FL}}} \sim \frac{g_{f,i}}{v_{0,i} \log 1/v_{0,i} }$, 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 $\Lambda$. The remarkable efficiency of the single collective field in hampering the screening of the impurity spin by the Fermi surface originates from a ultraviolet/infrared (UV/IR) mixing: bosons with momenta up to a UV cutoff actively suppress Kondo screening at low energies.