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Register a new userRenormalization Group Approach to Anderson Impurity in the Bulk of Topological Insulators
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It has been recently suggested that when an Anderson impurity is immersed in the bulk of a topological insulator, a Kondo resonant peak will appear simultaneously with an in-gap bound-state when the band-dispersion has an inverted-Mexican-hat form. The mid-gap bound-state generates another spin state and the Kondo effect is thereby screened. In this paper we study this problem within a weak-coupling RG scheme where we show that the system exhibits complex crossover behavior between different symmetry configurations and may evolve into a self-screened-Kondo or SO(3) low energy fix point. Experimental consequences of this scenario are pointed out.
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Electron scattering off an Anderson impurity immersed in the bulk of a 3D topological insulator is studied in the strong coupling regime, where the temperature $T$ is lower than the Kondo temperature $T_K$. The system displays either a self-screened Kondo effect, or a Kondo effect with SO(3) or SO(4) dynamical symmetries. Low temperature Kondo scattering for systems with SO(3) symmetry displays the behavior of a singular Fermi liquid, an elusive property that so far has been observed only in tunneling experiments. This is demonstrated through the singular behavior as $T to 0$ of the specific heat, magnetic susceptibility and impurity resistivity, that are calculated using well known (slightly adapted) conformal field theory techniques. Quite generally, the low temperature dependence of some of these observables displays a remarkable distinction between the SO(n=3,4) Kondo effect, compared with the standard SU(2) one.
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multi-orbital Anderson impurity model. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene: (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis reveals that, for the particle-hole symmetric case at half filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening while the ground state of the other two models forms a spin singlet state. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence of absence of unscreened magnetic moment at the impurity site, the spin-spin correlation functions decay as $r^{-3}$, differently from the non-interacting limit ($r^{-2}$), for model (i) and as $ r^{-4}$, exactly the same as the non-interacting limit, for models (ii) and (iii) in the asymptotic $r$, where $r$ is the distance between the impurity site and the conduction site.
Critical transition points between symmetry-broken phases are characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that traces out the large momentum modes, this well known fact can break down in non-Hermitian systems. Based on non-Hermitian Su-Schrieffer-Hegger (SSH)-type models, we propose a real-space decimation scheme to study the criticality between the topological and trivial phase. We provide concrete examples and an analytic proof to show that the real-space scheme perfectly overcomes the insufficiency of the standard method, especially in the sense that it always preserves the system at criticality as fixed points under RG. The proposed method can also greatly simplify the search of critical points for complicated non-Hermitian models by ruling out the irrelevant operators. These results pave the way towards more advanced RG-based techniques for the interacting non-Hermitian quantum systems.
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green functions and allows for a more accurate calculation of equilibrium spectral functions, than is possible directly from the one-particle Green function [Bulla {it et al.} Journal of Physics: Condensed Matter {bf 10}, 8365 (1998)], for example, within the numerical renormalization group method. In addition, the self-energy itself is a central quantity required in the dynamical mean field theory of strongly correlated lattice models. Here, we show how to generalize the self-energy method to the time-dependent situation for the prototype model of strong correlations, the Anderson impurity model . We use the equation of motion method to obtain closed expressions for the local Green function in terms of a time-dependent correlation self-energy, with the latter being given as a ratio of a two- and a one-particle time-dependent Green function. We benchmark this self-energy approach to time-dependent spectral functions against the direct approach within the time-dependent numerical renormalization group method. The self-energy approach improves the accuracy of time-dependent spectral function calculations, and, the closed form expressions for the Green function allow for a clear picture of the time-evolution of spectral features at the different characteristic time-scales. The self-energy approach is of potential interest also for other quantum impurity solvers for real-time evolution, including time-dependent density matrix renormalization group and continuous time quantum Monte Carlo techniques.
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