David Logan

Abstract:

The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spectra in either phase and that at the QCP is explored in detail.

Abstract:

The periodic Anderson model (PAM) captures the essential physics of heavy fermion materials. Yet even for the paramagnetic metallic phase, a practicable many-body theory that can simultaneously handle all energy scales while respecting the dictates of Fermi liquid theory at low energies, and all interaction strengths from the strongly correlated Kondo lattice through to weak coupling, has remained quite elusive. Aspects of this problem are considered in the present paper where a non-perturbative local moment approach (LMA) to single-particle dynamics of the asymmetric PAM is developed within the general framework of dynamical mean-field theory. All interaction strengths and energy scales are encompassed, although our natural focus is the Kondo lattice regime of essentially localized f-spins but general conduction band filling, characterised by an exponentially small lattice coherence scale ωL. Particular emphasis is given to the resultant universal scaling behaviour of dynamics in the Kondo lattice regime as an entire function of ω′ = ω/ωL, including its dependence on conduction band filling, f-level asymmetry and lattice type. A rich description arises, encompassing both coherent Fermi liquid behaviour at low-ω′ and the crossover to effective single-impurity scaling physics at higher energies - but still in the ω/ωL,-scaling regime, and as such incompatible with the presence of two-scale 'exhaustion physics, which is likewise discussed.

Abstract:

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. © EDP Sciences, Società, Italiana di Fisica, Springer-Verlag 2003.

Abstract:

The pseudogap Anderson impurity model provides a paradigm for understanding local quantum phase transitions, in this case between generalised Fermi liquid (GFL) 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 D(ω). 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.