Composite Spin-Triplet Superconductivity in an SU(2)⊗SU(2)SU(2)\otimes SU(2) Symmetric Lattice Model

The two-channel Anderson lattice model which has $SU(2)\otimes SU(2)$ symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U$_{1-x}$Th$_x$Be$_{13}$ or Pr base skutterudite compounds such as PrFe$_4$P$_{12}$ or PrOs$_4$Sb$_{12}$. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as $|\omega|$ close to $\omega=0$. In the strong intermediate valent regime, the gap function acquires an additional \k-dependence.Comment: 20 pages, 12 figures, latex EPJ format. Accepted for publication as Eur.Phys.J.

Comment on "Scaling feature of magnetic field induced Kondo-peak splittings"

In a recent work Zhang and coworkers (PRB 82, 075111 (2010)) studied the Zeeman splitting of the Kondo resonance for the single impurity Anderson model in a finite magnetic field $B$ with the numerical renormalization group (NRG) method. There, it was found that with increasing magnetic field $B$ the position of the Kondo resonance in the total spectral function \textit{does not} approach its position in the spin resolved spectral function. Additionally, the position of the Kondo maximum exceeded the Zeeman energy for $B/ T_K\gtrsim 5-10$, where $T_K$ is the low energy Kondo scale of the model ($g=2$, $\mu_B=k_B=\hbar=1$). In this comment we argue that both these findings are produced by an improper choice of NRG parameter values. However, we reproduce the crossover in the splitting from Kondo-like behavior to a non-universal splitting larger than the Zeeman energy, but this crossover occurs at much larger fields of the order of the charge scale.Comment: Minor revisions; same version as publishe

On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems

We propose a numerical renormalization group (NRG) approach to steady-state currents through nano-devices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias $V$. We employ the time-dependent NRG to evolve the known steady-state density operator for a non-interacting junction into the density operator of the fully interacting nano-device at finite bias. We calculate the temperature dependent current as function of $V$ and applied external magnetic field using a recently developed algorithm for non-equilibrium spectral functions.Comment: 4 pages, 6 figure

Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a single energy scale only, due to the presence of a non-trivial quantum phase transition. In the strongly sub-ohmic regime, s<<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase - this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.Comment: 4 pages, 6 figures; final version, as publishe