Magnetic Quantum Phase Transitions in Kondo Lattices

Abstract

The identification of magnetic quantum critical points in heavy fermion metals has provided an ideal setting for experimentally studying quantum criticality. Motivated by these experiments, considerable theoretical efforts have recently been devoted to reexamine the interplay between Kondo screening and magnetic interactions in Kondo lattice systems. A local quantum critical picture has emerged, in which magnetic interactions suppress Kondo screening precisely at the magnetic quantum critical point (QCP). The Fermi surface undergoes a large reconstruction across the QCP and the coherence scale of the Kondo lattice vanishes at the QCP. The dynamical spin susceptibility exhibits $\omega /T$ scaling and non-trivial exponents describe the temperature and frequency dependence of various physical quantities. These properties are to be contrasted with the conventional spin-density-wave (SDW) picture, in which the Kondo screening is not suppressed at the QCP and the Fermi surface evolves smoothly across the phase transition. In this article we discuss recent microscopic studies of Kondo lattices within an extended dynamical mean field theory (EDMFT). We summarize the earlier work based on an analytical $\epsilon$-expansion renormalization group method, and expand on the more recent numerical results. We also discuss the issues that have been raised concerning the magnetic phase diagram. We show that the zero-temperature magnetic transition is second order when double counting of the RKKY interactions is avoided in EDMFT.

10 pages, 4 figures; references added; as published in JPCM in early September, except for the correction to the legend for Figure 1

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• Global Magnetic Phase Diagram and Local Quantum Criticality in Heavy Fermion Metals
• Heavy-electron quantum criticality and single-particle spectroscopy
• Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions
• Kondo Destruction and Quantum Criticality in Kondo Lattice Systems
• Quasiparticles beyond the Fermi liquid and heavy fermion criticality
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• Cellular Dynamical Mean Field Theory of the Periodic Anderson Model
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• Zero-Temperature Magnetic Transition in an Easy-Axis Kondo Lattice Model
• Magnetic quantum phase transition in an anisotropic Kondo lattice
• Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
• Spin Path Integrals, Berry phase, and the Quantum Phase Transition in the sub-Ohmic Spin-boson Model
• Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
• Cluster Extended Dynamical Mean Field Approach and Unconventional Superconductivity
• Local Quantum Criticality of a One-Dimensional Kondo Insulator Model