Spin and charge criticality in the pseudogap two-impurity Anderson model

Kondo screening of a magnetic impurity in a Fermi gas can be suppressed if the fermion-bath density of states follows a pseudogap power law. This leads to a Kondo-breakdown quantum phase transition. Non-Fermi liquid behavior arises due to critical local-moment fluctuations in both spin and charge sectors. Here, we study a two-impurity Anderson model with a pseudogap where the interactions between the two impurities can drive additional transitions into phases with inter-moment order. We utilize perturbative renormalization-group techniques to map out the phase diagram and to study the various quantum phase transitions. For the critical fixed points, we obtain analytical results for correlation-length exponents and anomalous dimensions of physical observables. We discuss realizations in quantum-dot systems.