Single-particle dynamics of the Anderson model: a two-self-energy description within the numerical renormalization group approach

Single-particle dynamics of the Anderson impurity model are studied using both the numerical renormalization group (NRG) method and the local moment approach (LMA). It is shown that a 'two-self-energy' description of dynamics inherent to the LMA, as well as a conventional 'single-self-energy' description, arise within NRG; each yielding correctly the same local single-particle spectrum. Explicit NRG results are obtained for the broken symmetry spectral constituents arising in a two-self-energy description, and the total spectrum. These are also compared to analytical results obtained from the LMA as implemented in practice. Very good agreement between the two is found, essentially on all relevant energy scales from the high-energy Hubbard satellites to the low-energy Kondo resonance.Comment: 12 pages, 6 figure

Magnetic properties of the Anderson model: a local moment approach

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.Comment: 7 pages, 3 postscript figues. Latex 2e using the epl.cls Europhysics Letters macro packag

Spectral scaling and quantum critical behaviour in the pseudogap Anderson model

The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid and local moment phases, via the local moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi liquid, interacting nature of the fixed point.Comment: 7 pages, 2 figure

Kondo insulators in the periodic Anderson model: a local moment approach

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.Comment: 15 pages, 10 postscript figures, accepted for publication in EPJ B; HyperTex disable

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.Comment: 14 pages, 6 figure

Quantum phase transition in capacitively coupled double quantum dots

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid `charge-ordered' phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.Comment: 4 pages, 3 figure

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations

BCS - BEC crossover at T=0: A Dynamical Mean Field Theory Approach

We study the T=0 crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory(DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field theory, usually used to describe this crossover, and to explore physics beyond it. Quantum fluctuations are incorporated using iterated perturbation theory as the DMFT impurity solver. We find that these fluctuations lead to large quantitative effects in the intermediate coupling regime leading to a reduction of both the superconducting order parameter and the energy gap relative to the HFB results. A qualitative change is found in the single-electron spectral function, which now shows incoherent spectral weight for energies larger than three times the gap, in addition to the usual Bogoliubov quasiparticle peaks.Comment: 11 pages,12 figures, Published versio

Magnetic field effects in few-level quantum dots: theory, and application to experiment

We examine several effects of an applied magnetic field on Anderson-type models for both single- and two-level quantum dots, and make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side the focus is on magnetization, single-particle dynamics and zero-bias conductance, with emphasis on the universality arising in strongly correlated regimes; including a method to obtain the scaling behavior of field-induced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior; and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field-dependence of the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from experiment occurring at fields in excess of $\sim$ 5 T, indicating the eventual inadequacy of using the equilibrium single-particle spectrum to calculate the conductance at finite bias.Comment: 15 pages, 12 figures. Version as published in PR