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

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 $\frac{\log Λ/T_K^{\mathrm{AFQCM}}}{\log Λ/T_K^{\mathrm{FL}}} \sim \frac{g_{f,i}}{v_{0,i} \log 1/v_{0,i} }$, 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 $Λ$. 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.

Figures (7)

• Figure 1: ($a$) In AFQCM, the hot spots (red dots) connected by the antiferromagnetic wave-vector $\vec{Q}_{AF}$ are strongly coupled with the boson that represents critical spin fluctuations. $v_0$, which represents the nesting angle between the pairs of hot spots connected by $\vec{Q}_{AF}$, determines the low-energy dynamics of the clean AFQCM. ($b$) The electron-impurity coupling ($J$) and boson-impurity coupling ($g_f$) cause the impurity spin to flip by creating a particle-hole excitation and a boson, respectively, while the latter two are strongly mixed through the electron-boson coupling ($g$). ($c$) The Kondo temperature vanishes in the small $v_0$ limit due to the dressing of the impurity by the critical spin fluctuations subject to strong UV/IR mixing.
• Figure 2: RG flow of the $\tilde{J}^V$ and $g_f$. The blue box zooms into the RG flow at short distances. For $\ell \leq \ell_f$, the large boson-impurity coupling suppresses the Kondo coupling, making it decrease with increasing length scale. For $\ell > \ell_f$, the boson-impurity coupling becomes subdominant, and the Kondo coupling begins to grow as in Fermi liquids. However, the suppressed Kondo coupling at $\ell_f$ greatly increases the length scale below which the Kondo coupling becomes $O(1)$.
• Figure 3: Logarithmic Kondo scale of the AFQCM relative to that of the Fermi liquid with the same electronic density of state and bare Kondo coupling plotted as a function of the bare boson-impurity coupling, $g_{f,i}$ for three different bare nesting angles $v_{0,i}$. The dashed lines represent the numerical solutions of Eqs. \ref{['eq:betag']} and \ref{['eq5']} obtained with $\tilde{J}^V_i = 10^{-8}$, and the solid lines are $\frac{\ell^{\mathrm{AFQCM}}}{\ell^{\mathrm{FL}}}= A \frac{g_{f,i}}{v_{0,i} \log (1/v_{0,i})}$ with $A = \frac{8 e^{3/4}}{3\sqrt{\pi }}$.
• Figure 4: ($\color{blue}a$) The inverse propagator of the peudo-fermion. (${\color{blue}b}$) The boson-impurity vertex. (${\color{blue}c}$) The electron-impurity vertex. Here, the double wiggly lines, the dashed lines, and the solid lines represent the boson propagators, the pseudo-fermion propagators and the electron propagators, respectively.
• Figure 5: The one-loop diagrams that renormalize the pseudo-fermion, the boson-impurity coupling and the Kondo coupling. (${\color{blue}a}$) The psuedo-fermion self energy. (${\color{blue}b}$) The boson-impurity vertex correction. (${\color{blue}c}$-${\color{blue}e}$) The vertex correction for the Kondo coupling. The boson propagator is non-perturbatively dressed by particle-hole excitations.