Magnetic Quantum Phase Transitions in Kondo Lattices

TL;DR

This paper reviews recent theoretical advances in understanding magnetic quantum phase transitions in Kondo lattices, emphasizing the local quantum critical scenario and contrasting it with the spin-density-wave picture, supported by EDMFT studies.

Contribution

It provides a comprehensive overview of microscopic EDMFT studies on Kondo lattices, clarifying the nature of quantum critical points and the role of magnetic interactions.

Findings

Zero-temperature magnetic transition is second order when RKKY double counting is avoided.

Fermi surface reconstruction occurs at the QCP in the local quantum critical picture.

Dynamical spin susceptibility exhibits $/T$ scaling and non-trivial exponents.

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.