Analytic theory of Hund's metals: A renormalization group perspective

We study the emergence of quasiparticles in Hund's metals with an $\mathrm{SU}\left(M\right)\times \mathrm{SU}\left(N\right)$-symmetric Kondo impurity model carrying both spin and orbital degrees of freedom. We show that the coupling of the impurity spin to the conduction electrons can be ferromagnetic, notably for hole-doped iron pnictides. We derive the weak-coupling renormalization group (RG) equations for arbitrary representations of $\mathrm{SU}\left(M\right)\times \mathrm{SU}\left(N\right)$. A ferromagnetic spin coupling results in a protracted RG flow, accounting for the surprising particle-hole asymmetry that is observed in the iron-pnictide systems. We establish the low coherence scale $T_{\mathrm{K}}$, which depends on the filling through the impurity representation. We also discuss the temperature dependence of the spin and orbital susceptibilities. Finally, we argue that this mechanism explains the strong valence dependence of the coherence scale observed in dilute transition-metal magnetic alloys.

Figure 1

Young's tableaux of the representations of $\mathbf{T}$ and $\mathbf{S}$ in our class of Hund's metals. A single box represents a fundamental spin of $\mathrm{SU}\left(M\right)$ or $\mathrm{SU}\left(N\right)$.

Figure 2

(Top) Second- and third-order nonparquet diagrams contributing to the RG equations (8)–(10). (Bottom) Third-order renormalization of the wave function and a fourth-order diagram.

Figure 3

Numerical RG flow starting from (a) weakly ferromagnetic $|J_0|={10}^{-3}\lesssim K_0$, (b) strongly ferromagnetic $|J_0|={10}^{-1}\gg K_0$, and (c) strongly antiferromagnetic $J_0={10}^{-2}\gg K_0$ $\left(q=3/2,d=1,K_0={10}^{-3},I_0={10}^{-5},N=20\right)$.