Perturbative Kondo destruction and global phase diagram of heavy fermion metals

Abstract

Strange metals represent a foundational problem in quantum condensed matter physics, and heavy fermion systems provide a canonical setting to advance a general understanding. The concept of a Kondo destruction quantum critical point is widely invoked to describe the competition of the Kondo effect and the local-moment magnetism. Here, we develop a unified field-theoretic approach, analyzing this competition from a rare approach that is anchored by the magnetically ordered side. Our analysis reveals, for the first time within a renormalization group framework, a quantum critical point across which the Kondo effect goes from being destroyed to dominating. Our findings elucidate not only the Kondo destruction quantum criticality but also an accompanying global phase diagram of heavy fermion metals.

Figures (10)

• Figure 1: Proposed global phase diagram for heavy fermion systems Paschen-Si_2020, where G is the degree of magnetic frustration and $J_K$ is the Kondo coupling. The paramagnetic ($P$) and antiferromagnetic ($AF$) phases, with Kondo screening ($L$) and destruction ($S$), reflect the competition between the Kondo and RKKY interactions. The lines describe the associated quantum phase transitions. For details, see the main text.
• Figure 2: Feynman rules of the action (\ref{['model']}) after rescaling $\vec{\pi}\rightarrow\sqrt{g}\vec{\phi}$, where $\alpha=x,y$. The solid arrow line and the wavy line are the propagators of the fermionic and bosonic field respectively. The slash and dot on the bosonic propagators denote the space and time derivative respectively. Expansion to higher orders contains vertices with more boson legs, where the leading order of them still contributes to (c) and (d) through vertex corrections. We summarize the vertex corrections from higher order vertices through Supplementary Materials sm.
• Figure 3: Singular one-loop diagrams for (a,b) bosonic propagator (c) for fermion propagator for transverse Kondo coupling.
• Figure 4: Vertex corrections at one loop level. Only the diagrams shown here contribute non-trivially to the beta function; other topologically possible one-loop diagrams vanish (see Supplementary Material, Fig. S4 for the complete classification)
• Figure 5: RG flow of $g$ and $\lambda$ for $v/c<(\sqrt{2}-1)/2$, where the gray dot represents the AF fixed point, and the purple dot denotes the QCP of QNL$\sigma$M at $g^*=\epsilon$. The orange and blue dots denote for multicritical point and Kondo destruction critical point.