We consider an Anderson impurity model in which the locally correlated orbital is coupled to a host with a gapped density of states. Single-particle dynamics are studied, within a perturbative framework that includes both explicit second-order perturbation theory and self-consistent perturbation theory to all orders in the interaction. Away from particle-hole symmetry the system is shown to be a generalized Fermi liquid (GFL) in the sense of being perturbatively connectable to the non-interacting limit; and the exact Friedel sum rule for the GFL phase is obtained. We show by contrast that the particle-hole symmetric point of the model is not perturbatively connected to the non-interacting limit, and as such is a non-Fermi liquid for all non-zero gaps. Our conclusions are in agreement with NRG studies of the problem.
The Friedel oscillations in the vicinity of a Friedel-Anderson (FA) impurity are investigated numerically. For an FA impurity in the local moment limit the normalized amplitude A(ξ) is S-shaped, approximately zero at short distances, approaching two at large distances and crossing the value one at the characteristic length ξ_{1/2}. Surprisingly, the Friedel oscillations of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level show a very similar behavior of their amplitude A(ξ). A comparison correlates the resonance width and the Kondo energy of the FA impurity w…
The twofold degenerate Anderson impurity model [1-4] is investigated and the strong electronic correlations of d-electrons of impurity ion are taken into account by elaborating suitable diagram technique. We discuss the properties of the Slater-Kanamori model [2-4] of d-impurity electrons. After finding the eigenfunctions and eigenvalues of all 16 local states, we determine the local one-particle propagator. Then we construct the perturbation theory around the atomic limit of the impurity ion and obtain the Dyson type equation for the renormalized one-particle propagator. Diagrammatic theory h…
We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, corresponding respectively to an overlapping and gapped energy spectra of the set of bath states. We find that with an approp…
We show that a generic single-orbital Anderson impurity model, lacking for instance any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridisation is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetisation of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value $R_\text{W}=2$ in the Kondo r…
We develop a continuous-time quantum Monte Carlo method based on a strong-coupling expansion for Anderson impurity models with phonon-assisted hybridizations for arbitrary number of phonon modes. As a benchmark, we investigate the two-channel Anderson model with a single phonon, and numerically demonstrate that an SO(5) susceptibility composed of localized-electron charge and phonon-parity operators diverges logarithmically at the non-Fermi liquid critical point in the model, which verifies the predictions by the boundary conformal field theory[K. Hattori: Phys. Rev. B {\bf 85} (2012) 214411].
The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature $T_K$. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small fnite parameters at arbitrarily small…
In the two-impurity Anderson model, the inter-impurity spin exchange interaction favors a spin singlet state between two impurities leading to the breakdown of the Kondo effect. We show that a local uniform magnetic field can delocalize the quasiparticles to restore the Kondo resonance. This transition is found to be continuous, accompanied by not only the divergence of the staggered (antiferromagnetic) susceptibility, but also the divergence of the uniform spin susceptibility. This may imply that the magnetic field induced quantum phase transitions in Kondo systems are in favor of the local c…
We implement the Lanczos algorithm on natural orbital basis to solve the zero-temperature Green's function of Anderson impurity models, following the work of Y. Lu, M. Höppner, O. Gunnarsson, and M. W. Haverkort, Phys. Rev. B {\bf 90} (2014) 085102. We present the technical details, generalize the algorithm to the cases of particle-hole asymmetry, with local magnetic field, and of two impurities. The results are benchmarked with conventional Lanczos, quantum Monte Carlo, and numerical renormalization group methods, demonstrating its potential as a powerful impurity solver for the dynamical mea…
We study the property of a magnetic impurity on a single-layer graphene within an Anderson impurity model. Due to the vanishing local density of states at the Fermi level in graphene, the impurity spin cannot be effectively screened out. Treating the problem within the Gutzwiller approximation, we found a region in the parameter space of $U$-$E^f$ where the impurity is in the local moment state, which is characterized by a zero effective hybridization between the bath electron and the magnetic impurity. Here $U$ is the onsite Coulomb repulsion of the impurity electrons and $E^f$ the impurity e…
We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.
We demonstrate the effectiveness of a generalized renormalized perturbational approach to calculate the induced magnetization for the single impurity Anderson model with a strong on-site interaction, using flow equations for renormalized parameters to scale from a weak correlation to a strong correlation regime. We show that, using simple approximation schemes in different parameter regimes, remarkably accurate results can be obtained for all magnetic field values by comparing the results with those from direct numerical renormalization group and Bethe ansatz calculations.
Ground-state properties of the non-interacting symmetric single-impurity Anderson model (SIAM) are derived from the corresponding eigenenergy equation. Explicit formulae are given for the ground-state energy, the hybridization, and the momentum distribution that are essential quantities for variational approaches to the interacting model. Various spectral functions, e.g., the total density of states, the phase shift function, and the impurity spectral function, are shown to agree with those obtained from the equation-of-motion method (see supplementary material). For a constant hybridization s…
In this work we outline a simple and numerically inexpensive approach to describe the spectral features of the single-impurity Anderson model. The method combines aspects of the density matrix embedding theory (DMET) approach with a spectral broadening approach inspired by those used in numerical renormalization group (NRG) methods. At zero temperature for a wide range of U , the spectral function produced by this approach is found to be in good agreement with general expectations as well as more advanced and complex numerical methods such as DMRG-based schemes. The theory developed here is si…
We study the quench dynamics of an Anderson impurity model using the configuration interaction (CI) method. In particular, we focus on the relaxation behavior of the impurity occupation. The system is found to behave very differently in the weak-coupling and strong-coupling regimes. In the weak-coupling regime, the impurity occupation relaxes to a time-independent constant quickly after only a few oscillations. In the strong-coupling regime, the impurity occupation develops a fast oscillation, with a much slower relaxation. We show that it is the multi-peak structure in the many-body energy sp…
Using non-equilibrium renormalized perturbation theory, we calculate the conductance G as a function of temperature T and bias voltage V for an Anderson model, suitable for describing transport properties through a quantum dot. For renormalized parameters that correspond to the extreme Kondo limit, we do not find a simple scaling formula beyond a quadratic dependence in T and V. However, if valence fluctuations are allowed, we find agreement with recent experiments.
The density matrix renormalization group method is applied to obtain the ground state phase diagram of the single impurity Anderson model on the honeycomb lattice at half filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparis…
A particle-hole symmetric Anderson impurity model with a metallic host of narrow bandwidth is studied within the framework of the local moment approach. The resultant single-particle spectra are compared to unrestricted Hartree-Fock, second order perturbation theory about the noninteracting limit, and Lanczos spectra by Hofstetter and Kehrein. Rather accurate analytical results explain the spectral evolution over almost the entire range of interactions. These encompass, in particular, a rationale for the four-peak structure observed in the low-energy sector of the Lanczos spectra in the modera…
We study the spin magnetic moment of a single impurity embedded in a finite-size non-magnetic host exhibiting a band gap. The calculations were performed using a tight-binding model Hamiltonian. The simple criterion for the magnetic to non-magnetic transition as given in the Anderson impurity model breaks down in these cases. We show how the spin magnetic moment of the impurity that normally would be quenched can be restored upon introducing a gap at the Fermi level in the host density of states. The magnitude of the impurity spin magnetic moment scales monotonically with the size of the band …
We study the non-interacting two-impurity Anderson model on a lattice using the Green function equation-of-motion method. A case of particular interest is the RKKY limit that is characterized by a small hybridization between impurities and host electrons and the absence of a direct coupling between the impurities. In contrast to the low-density case, at half band-filling and particle-hole symmetry, the RKKY interaction decays as the inverse square of the impurity distance along the axis of a simple cubic lattice. In the RKKY limit, for the spectral function we generically observe a small split…
In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by a…
We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized interacting electron coupled to a bath of conduction electrons. Our approach uses an external magnetic field as flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices which are fixed by Ward identities. We calculate the quasi-particle residue and the spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with the Bethe ansatz result…
We present an alternative functional renormalization group (fRG) approach to the single-impurity Anderson model at finite temperatures. Starting with the exact self-energy and interaction vertex of a small system ('core') containing a correlated site, we switch on the hybridization with a non-interacting bath in the fRG-flow and calculate spectra of the correlated site. Different truncations of the RG-flow-equations and choices of the core are compared and discussed. Furthermore we calculate the linear conductance and the magnetic susceptibility as functions of temperature and interaction stre…
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 Anderso…
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. Expe…
We investigate a quantum dot (Anderson impurity) coupled to metallic leads, with a time-periodic voltage bias across the device. Using a time-dependent Schrieffer-Wolff transformation, we show that the Floquet Hamiltonian of the model can be mapped onto a two-channel Kondo model, in which the impurity is screened by separate conduction bands corresponding to parity-even and odd superpositions of the metallic leads. By changing the frequency and amplitude of the perturbation, one can tune the system to a quantum critical point with symmetric coupling of the impurity to both channels. For the un…
In this work we introduce a modified real-time continuous-time hybridization-expansion quantum Monte Carlo solver for a time-dependent single-orbital Anderson impurity model: CT-1/2-HYB-QMC. In the proposed method the diagrammatic expansion is performed only for one out of the two spin channels, while the resulting effective single-particle problem for the other spin is solved semi-analytically for each expansion diagram. CT-1/2-HYB-QMC alleviates the dynamical sign problem by reducing the order of sampled diagrams and makes it possible to reach twice as long time scales in comparison to the s…
Using the functional renormalization group (FRG) and the numerical renormalization group (NRG), we calculate the spectral function of the Anderson impurity model at zero and finite temperatures. In our FRG scheme spin fluctuations are treated non-perturbatively via a suitable Hubbard-Stratonovich field, but vertex corrections are neglected. A comparison with our highly accurate NRG results shows that this FRG scheme gives a quantitatively good description of the spectral line-shape at zero and finite temperatures both in the weak and strong coupling regimes, although at zero temperature the FR…
In a previous work (N. H. Tong, Phys. Rev. B 92, 165126 (2015)), an equation-of-motion based series expansion formalism was used to do the second-order strong-coupling expansion for the single-particle Green function of the Anderson impurity model. In this paper, we improve this theory in two aspects. We first use a more accurate scheme to self-consistently calculate the averages that appear in G1. In the resummation process, we use updated coefficients for the continued fraction, guided by the formally exact continued fraction from the Mori-Zwanzig theory. These changes lead to more accurate …
In this paper we have explored the role of valence fluctuations in an extended Anderson impurity model (e-SIAM) in which there is an additional Hubbard repulsion between conduction and impurity electrons, employing perturbative renormalization methods. We have calculated the scaling equations for the model parameters and solved them both analytically and numerically to find how valence fluctuations renormalize these parameters. Analytical solutions of the scaling equations yielded scaling invariants of the model which we find to be different than the Anderson impurity model signifying differen…
The Kondo resonance at the Fermi level is well-established for the electronic structure of Ce (f1 electron) and Yb (f1 hole) based systems. In this work, we report complementary experimental and theoretical studies on the Kondo resonance in Pr-based f2 system, PrTi2Al20. Using Pr 3d-4f resonant photoemission spectroscopy and single impurity Anderson model (SIAM) calculations including the full multiplets of Pr ions, we show that an f2 system can also give rise to a Kondo resonance at the Fermi level. The Kondo resonance peak is experimentally observed through a final-state-multiplet dependent …
