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Bulletin of the American Physical Society

Quantum Critical Behaviour Near the Kondo Breakdown Fixed Point

Indranil Paul, C. Pépin, Michael R. Norman

Published Mar 15, 2006• 0 citations
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arXiv:2005.10278•Physical Review Letters•Nov 13, 2020•23 citations
In this paper, we examine the dynamical charge-Kondo-breakdown scenario proposed for cuprate superconductors within the perspective of renormalization group (RG) topology. By analyzing the coupled RG flow equations governing the effective low-energy theory, we determine the fixed-point structure, stability properties, and global organization of the flow. We find that the putative finite-coupling interacting fixed point is unstable against perturbations transverse to an invariant critical manifold. As a result, generic RG trajectories exhibit runaway behavior. To elucidate the global structure of the theory, we combine analytical solutions of the flow equations with numerical phase portraits and Poincaré compactification. This analysis reveals that the interacting fixed point exhibits a marginally relevant instability, generating an exponentially large but finite crossover scale. The resulting flow topology closely resembles anisotropy-driven runaway flows encountered in fluctuation-induced weakly first-order transitions. Within this framework, the apparent quantum-critical regime can be understood as an extended crossover controlled by a near-critical fixed point, rather than by asymptotic scale invariance. The results obtained indicate that the existence of extended scaling behavior does not, by itself, imply the presence of a stable interacting quantum critical state. More generally, our analysis demonstrates how RG topology can provide a powerful diagnostic for distinguishing genuine criticality from pseudo-critical behavior in theories of strongly correlated quantum matter.
We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.