We propose a version of the functional renormalization-group (fRG) approach, which is, due to including Litim-type cutoff and switching off (or reducing) the magnetic field during fRG flow, capable of describing a singular Fermi-liquid (SFL) phase, formed due to the presence of local moments in quantum dot structures. The proposed scheme allows one to describe the first-order quantum phase transition from the ``singular'' to the ``regular'' paramagnetic phase with applied gate voltage to parallel quantum dots, symmetrically coupled to leads, and shows sizable spin splitting of electronic states in the SFL phase in the limit of vanishing magnetic field $H\ensuremath{\rightarrow}0$; the calculated conductance shows good agreement with the results of the numerical renormalization group. Using the proposed fRG approach with the counterterm, we also show that for asymmetric coupling of the leads to the dots the SFL behavior similar to that for the symmetric case persists, but with occupation numbers, effective energy levels, and conductance changing continuously through the quantum phase transition into the SFL phase.
We show that the traditional classification of quantum inpurity models based on thermodynamics is insufficient to probe the nature of their low-energy dynamics. We propose an analysis based on scattering theory, dividing Fermi liquids into regular Fermi liquids and singular Fermi liquids. In both cases electrons at the Fermi energy scatter elastically off the impurity, but in the case of regular Fermi liquids the scattering has analytical properties in the vicinity of the Fermi energy, while for singular Fermi liquids it does not, resulting in a breakdown of Nozi\`eres' Fermi-liquid picture and singular thermodynamic behavior. Using the Bethe ansatz and numerical renormalization group, we show that the ordinary Kondo model is a regular Fermi liquid whereas the underscreened Kondo model is a a singular Fermi liquid. Conventional regular Fermi liquid behavior is reestablished in an external magnetic field
H, but with a density of states which diverges as
1∕H. Our results may be relevant for the recently observed field-tuned quantum criticality in heavy electron materials.
We study a steady-state nonequilibrium transport between two interacting helical edge states of a two-dimensional topological insulator, described by helical Luttinger liquids, through a quantum dot. For a noninteracting dot, the current is obtained analytically by including the self-energy correction to the dot's Green function. For an interacting dot, we use the equation-of-motion method to study the influence of weak on-site Coulomb interaction on the transport. We find the metal-to-insulator quantum phase transition for attractive
or repulsive interactions in the leads when the magnitude of the interaction strength characterized by a charge sector Luttinger parameter
K goes beyond a critical value. The critical Luttinger parameter
Kcr depends on the hopping strengths between the dot and the leads, as well as the energy level of the dot with respect to the Fermi levels of the leads, ranging from the weak-interaction regime for the dot level off-resonance to the strong-interaction regime for the dot in resonance with the equilibrium Fermi level. Near the transition, there are various singular behaviors of current noise, dot density of state, and the decoherence rate (inverse of lifetime) of the dot, which are briefly discussed.