6 research outputs found
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
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
-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