David Logan

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 a 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 single-particle scaling spectrum and the self-energy.

Abstract:

We develop a local moment approach to static properties of the symmetric Anderson model in the presence of a magnetic field, focussing in particular on the strong-coupling Kondo regime. The approach is innately simple and physically transparent; but is found to give good agreement, for essentially all field strengths, with exact results for the Wilson ratio, impurity magnetization, spin susceptibility and related properties.

Abstract:

The symmetric Anderson impurity model with a hybridization vanishing at the Fermi level. ΔI ∝ |ωVBAR^r, is studied via the numerical renormalization group (NRG) at T = O; 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) ∝ |ωVBAR^r D(ω) are found to contain a generalized Kondo resonance that is ubiquitously pinned at the Fermi level; and which exhibits a characteristics 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-Sunjic tails, in agreement with LMA predictions.

Abstract:

We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength Δ0. Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behavior, Δ0Z/D≫1 and ≪1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ∑i(ω) is also examined beyond the confines of PT. It is argued that on frequency scales of order ω∼Δ0D, the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ∑i(ω) connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U.

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: ΔI α |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 spin-fluctuation 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 Uc(r) separating SC/LM states and the Kondo scale ωm(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-Šunjić tails in the wings of the Kondo resonance, as well as characteristic low-energy 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. © 2000 IOP Publishing Ltd.