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Register a new userWard identities for the Anderson impurity model: derivation via functional methods and the exact renormalization group
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Using functional methods and the exact renormalization group we derive Ward identities for the Anderson impurity model. In particular, we present a non-perturbative proof of the Yamada-Yosida identities relating certain coefficients in the low-energy expansion of the self-energy to thermodynamic particle number and spin susceptibilities of the impurity. Our proof underlines the relation of the Yamada-Yosida identities to the U(1) x U(1) symmetry associated with particle number and spin conservation in a magnetic field.
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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.
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 comparison, we also study the low-energy effective pseudogap Anderson model. Although the high-energy excitations are obviously different, we find that the ground state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single impurity Anderson model on the honeycomb lattice, thus providing the first quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally three fold degenerate at the valence fluctuating point. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the $varphi^4$ theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
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.
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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