Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling.

We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada and Yosida. It includes, partly, a microscopic clarification of the related achievements based on Nozières' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys. Rev. B 95, 165404 (2017)PRBMDO2469-995010.1103/PhysRevB.95.165404]. In our formulation, the Fermi-liquid parameters such as the quasiparticle energy, damping, and transport coefficients are related to each other through the total vertex Γ_{σσ^{'};σ^{'}σ}(ω,ω^{'};ω^{'},ω), which may be regarded as a generalized Landau quasiparticle interaction. We obtain exactly this function up to linear order with respect to the frequencies ω and ω^{'} using the antisymmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half filling through the nonlinear susceptibilities. We also apply the formulation to nonequilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field.

Convergence of energy scales on the approach to a local quantum critical point.

We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two-impurity Anderson model. The two impurities are coupled by an interimpurity exchange interaction J and direct interaction U{12} and are hybridized with separate conduction channels. The low energy behavior is described in terms of renormalized parameters. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor z→0, and the renormalized parameters can be expressed in terms of a single energy scale T{*}. The values of the renormalized interaction parameters in terms of T{*} can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation. These predictions are confirmed by the numerical renormalization group calculations, including the case when the on site interaction U=0.

A new renormalization group approach for systems with strong electron correlation.

The anomalous low energy behaviour observed in metals with strong electron correlation, such as in the heavy fermion materials, is believed to arise from the scattering of the itinerant electrons with low energy spin fluctuations. In systems with magnetic impurities this scattering leads to the Kondo effect and a low energy renormalized energy scale, the Kondo temperature T(K). It has been generally assumed that these low energy scales can only be accessed by a non-perturbative approach due to the strength of the local inter-electron interactions. Here we show that it is possible to circumvent this difficulty by first suppressing the spin fluctuations with a large magnetic field. As a first step field-dependent renormalized parameters are calculated using standard perturbation theory. A renormalized perturbation theory is then used to calculate the renormalized parameters for a reduced magnetic field strength. The process can be repeated and the flow of the renormalized parameters continued to zero magnetic field. We illustrate the viability of this approach for the single impurity Anderson model. The results for the renormalized parameters, which flow as a function of magnetic field, can be checked with those from numerical renormalization group and Bethe ansatz calculations.

Polaronic quasiparticles in a strongly correlated electron band.

We show that a strongly renormalized band of polaronic quasiparticle excitations is induced at the Fermi level of an interacting many-electron system on increasing the coupling of the electrons to local phonons. We give results for the local density of states at zero temperature both for the electrons and phonons. The polaronic quasiparticles satisfy Luttinger's theorem for all regimes considered, and their dispersion shows a kink similar to that observed experimentally in copper oxides. Our calculations are based on the dynamical mean field theory and the numerical renormalization group for the hole-doped Holstein-Hubbard model and large on-site repulsion.

Gap formation and soft phonon mode in the Holstein model.

We investigate electron-phonon coupling in many-electron systems using the dynamical mean-field theory in combination with the numerical renormalization group. This nonperturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.