Quantitative determination of the discretization and truncation errors in the numerical renormalization-group calculations of spectral functions

In the numerical renormalization group (NRG) calculations of the spectral functions of quantum impurity models, the results are affected by discretization and truncation errors. The discretization errors can be alleviated by averaging over different discretization meshes (z-averaging), but since each partial calculation is still performed for a finite discrete system, there are always some residual discretization and finite-size errors. The truncation errors affect the energies of the states and result in the displacement of the delta peak spectral contributions from their correct positions. The two types of errors are interrelated: for coarser discretization, the discretization errors increase, but the truncation errors decrease since the separation of energy scales in enhanced. In this work, it is shown that by calculating a series of spectral functions for a range of the total number of states kept in the NRG truncation, it is possible to estimate the errors and determine the error-bars for spectral functions, which is important when making accurate comparison to the results obtained by other methods and for determining the errors in the extracted quantities (such as peak positions, heights, and widths). The related spectral broadening issues are also discussed: it is shown that the overbroadening contorts the results without, surprisingly, reducing the variance of the curves. The method is applied to determine the error bounds in the Kondo peak splitting in the external magnetic field.Comment: 9 pages, 10 figures (in v2: new section on the high-field limit

Quantum impurity on the surface of a topological insulator

It is shown that the Hamiltonian for a quantum magnetic impurity on the surface of a topological insulator can be mapped to the conventional pseudo-gap Anderson impurity model, albeit with the combinations of continuum states which hybridize with the impurity having more complex structure in the reciprocal and spin space. If the Fermi level is away from the Dirac point, the impurity is predicted to be fully screened at low enough temperatures, i.e., there are no residual degrees of freedom.Comment: 4 pages; update to correspond to the published version + some typos corrected (missing minus sign in the transformation matrix

NRG calculations of the ground-state energy: application to the correlation effects in the adsorption of magnetic impurities on metal surfaces

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 approach is applied to study binding of magnetic adsorbates modeled by the Anderson-Newns model for chemisorption on metal surfaces. The correlation energy is largest in the valence-fluctuation regime; in the strong-coupling (Kondo) regime the Kondo-singlet formation energy is found to be only a minor contribution. As an application of the method to more difficult surface-science problems, we study the binding energy of a magnetic atom adsorbed near a step edge on a surface with a strongly modulated surface-state electron density. The zero-temperature magnetic susceptibility is determined from the field dependence of the binding energy, thereby providing an independent result for the Kondo temperature TK, which agrees very well with the TK extracted from a thermodynamic calculation.Comment: 4 page