A local moment approach to magnetic impurities in gapless Fermi systems

Abstract

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.

Dynamical Mean-Field Theory

“…Semi-analytic approximations such as the iterated perturbation theory (IPT) [31,48,33], the non-crossing approximation (NCA) [33,49], the fluctuation exchange approximation (FLEX) [50][51][52][53], the local moment approach (LMA) [54,55], and the parquet approximation [56] can also provide valuable insight.…”

Dynamical properties of the Anderson impurity model within a diagrammatic pseudoparticle approach

“…Approximation schemes for calculating G f,b which violate the gauge symmetry would, hence, violate the orthogonality of initial and final states, and should be expected to give incorrect results for physical quantities, even though certain aspects of the Fermi liquid fixed point can be described by symmetry-breaking approximations 32,33,34,35,36,37,38 . Therefore, we take great care to preserve the gauge symmetry.…”

Spectral scaling and quantum critical behaviour in the pseudogap Anderson model

“…This model has been studied extensively in recent years [3][4][5][6][7][8][9][10][11][12], especially for large-U where the low-energy subspace maps onto that of the Kondo model. It contains in general a non-trivial quantum phase transition at a finite U c ≡ U c (r); the quantum critical point (QCP) separating a degenerate local moment (LM) phase arising for U > U c , from a 'strong coupling' or generalized Fermi liquid (GFL) state [3][4][5][6][7][8][9][10][11][12] in which the impurity spin is locally quenched and a Kondo effect is manifest. As U → U c − the Kondo scale ω K vanishes and the local spectrum again exhibits universal ω/ω K -scaling [8,9].…”

“…Here we study single-particle dynamics of the pseudogap AIM [6,[8][9][10][11] via the local moment approach (LMA) [15], a physically motivated many-body theory that has already led [8] to new predictions for the problem, borne out by direct numerical renormalization group (NRG) calculations [9]. Our aims here, where we focus on the large-U Kondo regime of the symmetric model, are threefold.…”

“…The latter result is exact, generalizing to r > 0 behaviour well known for the metallic AIM r = 0 (where it amounts essentially trivially to satisfaction of the Friedel sum rule [2]). It embodies the fact [8,10] that the leading low-ω behaviour,…”