David Logan

Abstract:

The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.

Abstract:

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.

Abstract:

The paramagnetic phase of heavy fermion systems is investigated, using a non-perturbative local moment approach to the asymmetric periodic Anderson model within the framework of dynamical mean-field theory. The natural focus is on the strong coupling Kondo lattice regime wherein single-particle spectra, scattering rates, dc transport and optics are found to exhibit (ω/ωL,T/ωL) scaling in terms of a single underlying low-energy coherence scale ωL. Dynamics/transport on all relevant (ω,T) scales are encompassed, from the low-energy behaviour characteristic of the lattice coherent Fermi liquid, through incoherent effective single-impurity physics likewise found to arise in the universal scaling regime, to non-universal high-energy scales; and which description in turn enables viable quantitative comparison to experiment. © IOP Publishing Ltd.

Abstract:

Employing a local moment approach to the periodic Anderson model within the framework of dynamical mean-field theory, direct comparison is made between theory and experiment for the dc transport and optical conductivities of paramagnetic heavy fermion and intermediate valence metals. Four materials, exhibiting a diverse range of behaviour in their transport/optics, are analysed in detail: CeB6, Y bAl3, CeAl3 and CeCoIn 5. Good agreement between theory and experiment is in general found, even quantitatively, and a mutually consistent picture of transport and optics results. © IOP Publishing Ltd.

Abstract:

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.