Dynamical correlations in the spin-half two-channel Kondo model

Physical review. B, Condensed matter (Impact Factor: 3.66). 01/2008; 78(16). DOI: 10.1103/PhysRevB.78.165130
Source: arXiv


Dynamical correlations of various local operators are studied in the spin-half two-channel Kondo (2CK) model in the presence of channel anisotropy or external magnetic field. A conformal field theory-based scaling approach is used to predict the analytic properties of various spectral functions in the vicinity of the two-channel Kondo fixed point. These analytical results compare well with highly accurate density matrix numerical renormalization group results. The universal cross-over functions interpolating between channel-anisotropy or magnetic field-induced Fermi liquid regimes and the two-channel Kondo, non-Fermi liquid regimes are determined numerically. The boundaries of the real 2CK scaling regime are found to be rather restricted, and to depend both on the type of the perturbation and on the specific operator whose correlation function is studied. In a small magnetic field, a universal resonance is observed in the local fermion's spectral function. The dominant superconducting instability appears in the composite superconducting channel. Comment: 20 pages, 24 figures, PRB format

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    ABSTRACT: We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum impurity system. We illustrate the benefits of using non-Abelian symmetries by the example of calculations for the T-matrix of the two-channel Kondo model in the presence of magnetic field, for which conventional NRG methods produce large errors and/or take a long run-time. Comment: 12 pages, 6 figures, PRB format
    Physical review. B, Condensed matter 02/2008; 78(24). DOI:10.1103/PhysRevB.78.245109 · 3.66 Impact Factor
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    ABSTRACT: We study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-type exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one- and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes, as limiting cases, the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the interimpurity tunneling coupling. We point out that due to the existence of exponentially low-temperature scales, there is a parameter range where the stable “zero-temperature” fixed point is essentially never reached (not even in numerical renormalization group calculations). The zero-temperature conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction.
    Physical review. B, Condensed matter 06/2008; 77(24). DOI:10.1103/PhysRevB.77.245112 · 3.66 Impact Factor
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