Fractional Kondo state near a band singularity in one-dimensional systems

We present peculiar results for a Kondo state that is strongly affected by the proximity to the Fermi energy of a density of states ω^-1/2 singularity (located at the bottom of the band). Signs of this effect are already visible at the single-particle (non-interacting) level. Indeed, a resonant state ε_d (the Anderson impurity energy level), located close to the band singularity, suffers a strong 'renormalization', where a bound state ε_b (delta function) is created below the bottom of the band, while the impurity level ε_d is pushed up to a renormalized position ε_d^r. We note the very peculiar result that if ε_d is positioned right at the singularity, the spectral weight of the bound state ε_b is exactly 2/3. This is reminiscent of a result obtained for a three-dimensional electron gas subjected to a very strong spin-orbit interaction, treated in the continuum, as shown in PRB 93, 241111(R) (2016). The interacting system is modeled using the Single Impurity Anderson Model (SIAM), which is then solved using the Numerical Renormalization Group method. We provide a detailed description of the evolution of the Kondo state as the Fermi energy approaches the singularity, as well as when ε_d is placed at the singularity.