1,720,972 research outputs found
Energy resolution and discretization artifacts in the numerical renormalization group
No full textWe study the limits of the energy resolution that can be achieved in the calculations of spectral functions of quantum impurity models using the numerical renormalization group (NRG) technique with interleaving (z averaging). We show that overbroadening errors can be largely eliminated, that higher-moment spectral sum rules are satisfied to a good accuracy, and that positions, heights and widths of spectral features are well reproduced; the NRG approximates very well the spectral-weight distribution. We find, however, that the discretization of the conduction-band continuum nevertheless introduces artifacts. We present a modified discretization scheme which removes the band-edge discretization artifacts of the conventional approach and significantly improves the convergence to the continuum (Lambda -> 1) limit. Sample calculations of spectral functions with high energy resolution are presented. We follow in detail the emergence of the Kondo resonance in the Anderson impurity model as the electron-electron repulsion is increased, and the emergence of the phononic side peaks and the crossover from the spin Kondo effect to the charge Kondo effect in the Anderson-Holstein impurity model as the electron-phonon coupling is increased. We also compute the spectral function of the Hubbard model within the dynamical mean-field theory, confirming the presence of fine structure in the Hubbard bands
Numerical renormalization group study of two-channel three-impurity triangular clusters
No full textWe study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-type exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one- and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes, as limiting cases, the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the interimpurity tunneling coupling. We point out that due to the existence of exponentially low-temperature scales, there is a parameter range where the stable "zero-temperature" fixed point is essentially never reached (not even in numerical renormalization group calculations). The zero-temperature conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction
Anomaly in the heat capacity of Kondo superconductors
No full textUsing numerical renormalization group, we study thermodynamic properties of a magnetic impurity described by the Anderson impurity model in a superconducting host material described by the BCS Hamiltonian. When the Kondo temperature in the normal state, T-K, is comparable to the critical temperature of the superconducting transition, T-c, the magnetic doublet state may become degenerate with the Kondo singlet state, leading to a ln 3 peak in the temperature dependence of the impurity contribution to the entropy. This entropy increase translates into an anomalous feature in the heat capacity which might have already been experimentally observed.GWDG; German Science Foundation [SFB 602
Adaptive logarithmic discretization for numerical renormalization group methods
No full textThe problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi level) and it finds application, for example, in the numerical renormalization group (NRG) approach to quantum impurity problems (Kondo model), where the continuum of the conduction band states needs to be reduced to a finite number of levels with good sampling near the Fermi level. The discretization schemes under discussion are required to reproduce the original function after averaging over different interleaved discretization meshes, thus systematic deviations which appear in the conventional logarithmic discretization are eliminated. An improved scheme is proposed in which the discretization-mesh points themselves are determined in an adaptive way; they are denser in the regions where the function has higher values. Such schemes help in reducing the residual numeric artefacts in NRG calculations in situations where the density of states approaches zero over extended intervals. A reference implementation of the solver for the differential equations which determine the full set of discretization coefficients is also described
Spin-Fluctuation-Driven Superconductivity in the Kondo Lattice Model
No full textSuperconductivity in solids usually arises due to the generation of an attractive effective interaction between fermions close to the Fermi energy by some bosonic fluctuations. In the conventional theory, these are phonons, but in correlated electron systems like the cuprates or heavy fermions, one believes that the relevant bosonic degrees of freedom are the spin fluctuations. In this context, one usually argues that standard s-wave superconductivity cannot be formed as these spin fluctuations in general lead to a repulsive local interaction. Recently, we observed s-wave superconductivity in the Kondo lattice model using the dynamical mean-field approach. We can indeed show that this superconducting (SC) solution is due to local spin fluctuations arising from the Kondo effect. The reason for these fluctuations mediating an effective attractive interaction lies in the special properties of the heavy electron ground state, i.e., the formation of hybridized bands. Using a simple model, we can show that it is indeed an interband coupling that is largely responsible for the observed SC state. Such an observation is possibly rather interesting also concerning the situation in the pnictide superconductors
Properties of anisotropic magnetic impurities on surfaces
No full textUsing numerical renormalization-group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy DS(z)(2) terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy D and for any spin S, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin S and on the ratio D/T(K)((0)), where T(K)((0)) is the Kondo temperature in the absence of the anisotropy. For S=1, the screening occurs in two stages if D T(K)((0)). For negative anisotropy D, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy E(S(x)(2)-S(y)(2)) restores Fermi-liquid behavior in real systems
van Hove singularities in the paramagnetic phase of the Hubbard model: DMFT study
No full textUsing the dynamical mean-field theory (DMFT) with the numerical renormalization-group impurity solver we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional (3D) cubic lattice and the two-dimensional (2D) square lattice, as well as a DOS with inverse square-root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudogap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi-liquid behavior is recovered
Fine structure of spectra in the antiferromagnetic phase of the Kondo lattice model
No full textWe study the antiferromagnetic phase of the Kondo lattice model on bipartite lattices at half-filling using the dynamical mean-field theory with numerical renormalization group as the impurity solver, focusing on the detailed structure of the spectral function, self-energy, and optical conductivity. We discuss the deviations from the simple hybridization picture, which adequately describes the overall band structure of the system (four quasiparticle branches in the reduced Brillouin zone), but neglects all effects of the inelastic-scattering processes. These lead to additional structure inside the bands, in particular asymmetric resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic Kondo insulator quantum phase transition. These features, which we name "spin resonances," appear generically in all models where the f -orbital electrons are itinerant (large Fermi surface) and there is Neel antiferromagnetic order (staggered magnetization), such as periodic Anderson model and Kondo lattice model with antiferromagnetic Kondo coupling, but are absent in antiferromagnetic phases with localized f -orbital electrons (small Fermi surface), such as the Kondo lattice model with ferromagnetic Kondo coupling. The origin of the spin resonances is in the shifts of the resonance in the self-energy function in an order-parameter dependent way. We show that with increasing temperature and external magnetic-field the spin resonances become suppressed at the same time as the staggered magnetization is reduced. The optical conductivity sigma(Omega) has a threshold associated with the indirect gap, followed by a plateau of low conductivity and the main peak associated with the direct gap, while the spin resonances are reflected as a secondary peak or a hump close to the main optical peak. This work demonstrates the utility of high-spectral-resolution impurity solvers to study the dynamical properties of strongly correlated fermion systems
Unconventional Superconductivity from Local Spin Fluctuations in the Kondo Lattice
No full textThe explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to nonlocal fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation of heavy quasiparticle bands and the presence of strong local spin fluctuations. DOI: 10.1103/PhysRevLett.110.146406DFG [PR293/13-1]; BMBF [IND 10/067, FOR 960, GRK 1621]; ARRS [P1-0044
Many-particle effects in adsorbed magnetic atoms with easy-axis anisotropy: the case of Fe on the CuN/Cu(100) surface
No full textWe study the effects of the exchange interaction between an adsorbed magnetic atom with easy-axis magnetic anisotropy and the conduction-band electrons from the substrate. We model the system using an anisotropic Kondo model and we compute the impurity spectral function, which is related to the differential conductance (dI / dV) spectra measured using a scanning tunneling microscope. To make contact with the known experimental results for iron atoms on the CuN/Cu(100) surface (Hirjibehedin et al 2007 Science 317 1199), we calculated the spectral functions in the presence of an external magnetic field of varying strength applied along all three spatial directions. It is possible to establish an upper bound on the coupling constant J : in the range of the magnetic fields for which the experimental results are currently known (up to 7 T), the low-energy features in the calculated spectra agree well with the measured dI / dV spectra if the exchange coupling constant J is at most half as large as that for cobalt atoms on the same surface. We show that for an even higher magnetic field (between 8 and 9 T) applied along the 'hollow direction', the impurity energy states cross, giving rise to a Kondo effect which takes the form of a zero-bias resonance. The coupling strength J could be determined experimentally by performing tunneling spectroscopy in this range of magnetic fields. On the technical side, the paper introduces an approach for calculating the expectation values of global spin operators and all the components of the impurity magnetic susceptibility tensor (including the out-of-diagonal ones) in numerical renormalization group (NRG) calculations with no spin symmetry. An appendix contains a density functional theory (DFT) study of the Co and Fe adsorbates on the CuN/Cu(100) surface: we compare magnetic moments, as well as orbital energies, occupancies, centers and spreads, by calculating the maximally localized Wannier orbitals of the adsorbates.Slovenian Research Agency (ARRS) [Z1-2058]; DFG [SFB 602
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