Local quantum phase transition in the pseudogap Anderson model: scales, scaling and quantum critical dynamics

The pseudogap Anderson impurity model provides a paradigm for understanding local quantum phase transitions, in this case between generalised fermi liquid and degenerate local moment phases. Here we develop a non-perturbative local moment approach to the generic asymmetric model, encompassing all energy scales and interaction strengths and leading thereby to a rich description of the problem. We investigate in particular underlying phase boundaries, the critical behaviour of relevant low-energy scales, and single-particle dynamics embodied in the local spectrum. Particular attention is given to the resultant universal scaling behaviour of dynamics close to the transition in both the GFL and LM phases, the scale-free physics characteristic of the quantum critical point itself, and the relation between the two.Comment: 39 pages, 19 figure

Anderson impurities in gapless hosts: comparison of renormalization group and local moment approaches

The symmetric Anderson impurity model, with a soft-gap hybridization vanishing at the Fermi level with power law r > 0, is studied via the numerical renormalization group (NRG). Detailed comparison is made with predictions arising from the local moment approach (LMA), a recently developed many-body theory which is found to provide a remarkably successful description of the problem. Results for the `normal' (r = 0) impurity model are obtained as a specific case. Particular emphasis is given both to single-particle excitation dynamics, and to the transition between the strong coupling (SC) and local moment (LM) phases of the model. Scaling characteristics and asymptotic behaviour of the SC/LM phase boundaries are considered. Single-particle spectra are investigated in some detail, for the SC phase in particular. Here, the modified spectral functions are found to contain a generalized Kondo resonance that is ubiquitously pinned at the Fermi level; and which exhibits a characteristic low-energy Kondo scale that narrows progressively upon approach to the SC->LM transition, where it vanishes. Universal scaling of the spectra as the transition is approached thus results. The scaling spectrum characteristic of the normal Anderson model is recovered as a particular case, and is captured quantitatively by the LMA. In all cases the r-dependent scaling spectra are found to possess characteristic low-energy asymptotics, but to be dominated by generalized Doniach-Sunjic tails, in agreement with LMA predictions.Comment: 26 pages, 14 figures, submitted for publicatio

Magnetic Quantum Phase Transitions in Kondo Lattices

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