Magnetic quantum phase transitions in Kondo lattices

Abstract

The identification of magnetic quantum critical points in heavy fermion metals has provided anideal setting for experimentally studying quantum criticality. Motivated by theseexperiments, considerable theoretical efforts have recently been devoted to re-examiningthe interplay between Kondo screening and magnetic interactions in Kondo lattice systems.A local quantum critical picture has emerged, in which magnetic interactions suppressKondo screening precisely at the magnetic quantum critical point (QCP). The Fermisurface undergoes a large reconstruction across the QCP and the coherence scale of theKondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibitsω/T scaling and non-trivial exponents describe the temperature and frequency dependences ofvarious physical quantities. These properties are to be contrasted with the conventionalspin density wave picture, in which the Kondo screening is not suppressed at the QCP andthe Fermi surface evolves smoothly across the phase transition. In this article we discussrecent microscopic studies of Kondo lattices within an extended dynamical meanfield theory (EDMFT). We summarize the earlier work based on an analyticalϵ-expansion renormalization group method, and expand on the more recent numericalresults. We also discuss the issues that have been raised concerning the magnetic phasediagram. We show that the zero-temperature magnetic transition is second order whendouble counting of the Ruderman–Kittel–Kasuya–Yosida interactions is avoided inEDMFT.