Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution $chi_{textrm{imp}}$ to susceptibility, defined or
iginally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in $chi_{textrm{imp}}$, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility $chi_{textrm{loc}}$ and to compare them with $chi_{textrm{imp}}$ obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in $chi_{textrm{imp}}$ are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding $chi_{textrm{loc}}$ less accurate than $chi_{textrm{imp}}$, the FDM method allows a high-precision dynamical calculation of $chi_{textrm{loc}}$ at much reduced computational cost, with an accuracy at least one order higher than $chi_{textrm{imp}}$. Moreover, artifacts in the FDM algorithm to $chi_{textrm{imp}}$, and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilsons definition to such cases.
We propose a scheme to detect the Majorana bound states (MBSs) by a thermodynamically stable D.C. Josephson current with $4pi$-periodicity in the superconducting phase difference, which is distinct from the previous A.C. $4pi$-periodicity found in to
pological superconducting Josephson junctions. The scheme, consisting of a quantum dot coupled to two s-wave superconducting leads and a floating topological superconductor supporting two MBSs at its ends, only exploits the interplay of a local Zeeman field and the exotic helical and self-Hermitian properties of MBSs, without requiring the conservation of fermion parity and not relying on the zero-energy property of MBSs. Our D.C. $4pi$-periodicity is thus robust against the overlap between the two MBSs and various system parameters, including the local Coulomb interaction, the tunneling asymmetry, and the width of superconducting gap, which facilitates experimentally detection of the MBSs.
We investigate single-electron transport through quantum dots with negative charging energy induced by a polaronic energy shift. For weak dot-lead tunnel couplings, we demonstrate a bipolaronic blockade effect at low biases which suppresses the oscil
lating linear conductance, while the conductance resonances under large biases are enhanced. Novel conductance plateau develops when the coupling asymmetry is introduced, with its height and width tuned by the coupling strength and external magnetic field. It is further shown that the amplitude ratio of magnetic-split conductance peaks changes from 3 to 1for increasing coupling asymmetry. Though we demonstrate all these transport phenomena in the low-order single-electron tunneling regime, they are already strikingly different from the usual Coulomb blockade physics and are easy to observe experimentally.
We propose carbon nanotubes (CNTs) with magnetic impurities as a versatile platform to achieve unconventional Kondo physics, where the CNT bath is gapped by the spin-orbit interaction and surface curvature. While the strong-coupling phase is inaccess
ible for the special case of half-filled impurities in neutral armchair CNTs, the system in general can undergo quantum phase transitions to the Kondo ground state. The resultant position-specific phase diagrams are investigated upon variation of the CNT radius, chirality, and carrier doping, revealing several striking features, e.g., the existence of a maximal radius for nonarmchair CNTs to realize phase transitions, and an interference-induced suppression of the Kondo screening. We show that by tuning the Fermi energy via electrostatic gating, the quantum critical region can be experimentally accessed.
The Gamma-Dirichlet structure corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the
gamma process and vice versa. In this article, we begin with a brief review of existing results concerning the Gamma-Dirichlet structure. New results are obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. The laws of the gamma process and the Dirichlet process are the respective reversible measures of the measure-valued branching diffusion with immigration and the Fleming-Viot process with parent independent mutation. We view the relation between these two classes of measure-valued processes as the dynamical Gamma-Dirichlet structure. Other results of this article include the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration, and the establishment of the reversibility of the latter. One of these is related to an open problem by Ethier and Griffiths and the other leads to an alternative proof of the reversibility of the Fleming-Viot process.
