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A generalized Anderson model for a magnetic ion in a harmonic potential is formulated. The model is investigated by the numerical renormalization group(NRG) method. In addition to the conventional s-wave screening, the model exhibits phonon…
The symmetric Anderson impurity model, with a soft-gap hybridization vanishing at the Fermi level with power law r > 0, is studied via the numerical renormalization group (NRG). Detailed comparison is made with predictions arising from the…
We apply a functional implementation of the field-theoretical renormalization group (RG) method up to two loops to the single-impurity Anderson model. To achieve this, we follow a RG strategy similar to that proposed by Vojta \emph{et al.}…
We discuss the scale-free property of Wilson's numerical renormalization group(NRG) for the Kondo impurity problem. The single-particle state of the effective Hamiltonian with a cutoff $\Lambda$ is described by the wavepacket basis having…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
This article focuses on the calculation of spectral functions for single- and multi-impurity models using the density matrix renormalization group (DMRG). To calculate spectral functions from DMRG, the correction vector method is presently…
The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…
The anomalous low energy behaviour observed in metals with strong electron correlation, such as in the heavy fermion materials, is believed to arise from the scattering of the itinerant electrons with low energy spin fluctuations. In…
We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as rho(omega) \propto |omega|^r with r>0. We find two different fixed points: a local-moment fixed point…
Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i. e. using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the…
We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting…
The ground-state energy of a quantum impurity model can be calculated using the numerical renormalization group with a modified discretization scheme, with sufficient accuracy to reliably extract physical information about the system. The…
Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The…
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…
We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency…
Within the framework of the recently proposed Taylor-Lagrange regularization procedure, we reanalyze the calculation of radiative corrections in $QED$ at next to leading order. Starting from a well defined local bare Lagrangian, the use of…
We analyze the spectral function of the single-impurity two-terminal Anderson model at finite voltage using the recently developed diagrammatic quantum Monte Carlo technique as well as perturbation theory. In the (particle-hole-)symmetric…