A theory is developed for the single-particle spectra of the symmetric Anderson model, in which local moments are introduced explicitly from the outset. Dynamical coupling of single-particle processes to low-energy spin-flip excitations leads, within the framework of a two-self-energy description, to a theory in which both low-and high-energy spectral features are simultaneously captured, while correctly preserving Fermi liquid behaviour at low energies. The atomic limit, non-interacting limit and strong-coupling behaviour of the spectrum are each recovered. For strong coupling in particular, both the exponential asymptotics of the Kondo resonance and concomitant many-body broadening of the Hubbard satellite bands are shown to arise naturally within the present approach.

Abstract. A local moment approach is developed for single-particle excitations of a symmetric Anderson impurity model (AIM) with a soft-gap hybridization vanishing at the Fermi level: ∆ I ∝ |ω| r , with r > 0. Local moments are introduced explicitly from the outset, and a two-self-energy description is employed in which single-particle excitations are coupled dynamically to low-energy transverse spin fluctuations. The resultant theory is applicable on all energy scales, and captures both the spinfluctuation regime of strong coupling (large-U ), as well as the weak coupling regime where it is perturbatively exact for those r-domains in which perturbation theory in U is non-singular. While the primary emphasis is on single-particle dynamics, the quantum phase transition between strong coupling (SC) and local moment (LM) phases can also be addressed directly; for the spin-fluctuation regime in particular a number of asymptotically exact results are thereby obtained, notably for the behaviour of the critical U c (r) separating SC/LM states and the Kondo scale ω m (r) characteristic of the SC phase. Results for both single-particle spectra and SC/LM phase boundaries are found to agree well with recent numerical renormalization group (NRG) studies; and a number of further testable predictions are made. Single-particle spectra are examined systematically for both SC and LM states; in particular, for all 0 ≤ r < 1 2 , spectra characteristic of the SC state are predicted to exhibit an r-dependent universal scaling form as the SC/LM phase boundary is approached and the Kondo scale vanishes. Results for the 'normal' r = 0 AIM are moreover recovered smoothly from the limit r → 0, where the resultant description of single-particle dynamics includes recovery of Doniach-Sunjić tails in the wings of the Kondo resonance, as well as characteristic lowenergy Fermi liquid behaviour and the exponential diminution with U of the Kondo scale itself. The normal AIM is found to represent a particular case of more generic behaviour characteristic of the r > 0 SC phase which, in agreement with conclusions drawn from recent NRG work, may be viewed as a non-trivial but natural generalization of Fermi liquid physics.

The symmetric Anderson impurity model with a hybridization vanishing at the Fermi level, ∆ I ∝ |ω| r , is studied via the numerical renormalization group (NRG) at T = 0; and detailed comparison 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, and likewise compared. 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 D(ω) are investigated in some detail, for the SC phase in particular. Here, in accordance with a recently established result, the modified spectral functions F (ω) ∝ |ω| r D(ω) 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, ω K (r), 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, that exemplifies behaviour characteristic of the SC phase generally, and which 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-Sunjić tails, in agreement with LMA predictions.

Abstract. We consider the universal scaling behaviour of the Kondo resonance in the strong coupling limit of the symmetric Anderson impurity model, using a recently developed local moment approach. The resultant scaling spectrum is obtained in closed form, and is dominated by long tails that in contrast to previous work are found to exhibit a slow logarithmic decay rather than power-law form, crossing over to characteristic Fermi liquid behaviour on the lowest energy scales. The resultant theory, while naturally approximate, is found to give very good agreement for essentially all frequencies with numerical renormalization group calculations of both the singleparticle scaling spectrum and the self-energy.

The quantum mechanics of energy flow in many-dimensional Fermi resonant systems has several connections to the theory of Anderson localization in disordered solids. We argue that in high dimensional and highly quantum mechanical systems the energy flow can be modeled as coherent transport on a locally but weakly correlated random energy surface. This model exhibits a sharp but continuous transition from local to global energy flow characterized by critical exponents. Dephasing smears the transition and an interesting nonmonotonic dependence of energy flow rate on environmental coupling is predicted to occur near the transition.