Effective low-energy models for superconducting impurity systems

We present two complementary methods to calculate the Andreev bound state energies of a single-level quantum dot connected to superconducting leads described by the superconducting impurity Anderson model. The first method, which is based on a mapping to a low-energy model, can be utilized to extract the Andreev bound state energies from finite-temperature, imaginary-time quantum Monte Carlo data without the necessity of any analytic continuation technique. The second method maps the full model on an exactly solvable superconducting atomic limit with renormalized parameters. As such, it represents a fast and reliable method for a quick scan of the parameter space. We demonstrate that after adding a simple band correction this method can provide predictions for measurable quantities, including the Josephson current, that are in a solid quantitative agreement with precise results obtained by the numerical renormalization group and quantum Monte Carlo.Comment: 16 pages, 7 figure

Critical behavior in self-consistent conserving approximations of correlated electrons

We disclose a serious deficiency of the self-consistent conserving approximations of strongly correlated electron systems. There are two vertices, the divergence of each indicates a phase instability. We show that they generically display incomplete and mutually inconsistent critical behavior at different critical points. The dynamical vertex from the Schwinger-Dyson equation cannot be continued beyond its singularity since it does not obey the Ward identity and results in non-conserving response functions. The divergence in the conserving vertex, obeying the conservation laws, does not invoke a critical behavior of the spectral function and the specific heat. We demonstrate this ubiquitous ambiguity on an example of the single-impurity Anderson model. The dynamical vertex leads to strong coupling asymptotics with a logarithmic Kondo scale, while the conserving vertex results in magnetic instability of a spin-symmetric solution at a finite interaction strength.Comment: 5 pages, 2 figures, 1 Supplemental Materia

Second Order Perturbation Theory for a Superconducting Double Quantum Dot

We extend our approach based on the second order perturbation theory in the Coulomb interaction recently developed for quantum dots coupled to superconducting leads to the superconducting double quantum dot setups. Using our perturbative method we evaluate several single-particle quantities such as on-dot induced gap and generalized occupations together with the Andreev in-gap spectra and compare them with numerically exact results from the Numerical Renormalization Group and Quantum Monte Carlo finding a very good correspondence for not too strongly correlated regimes. Thus we can offer in a wide parameter range this method as an efficient and reliable alternative to the heavy numerical tools exclusively used so far for the description of such experimentally relevant systems.Comment: 8 pages, 4 figures, proceedings of the SCES 2019 conferenc