Superconductivity in the Kondo lattice model

We study the Kondo lattice model with additional attractive interaction between the conduction electrons within the dynamical mean-field theory using the numerical renormalization group to solve the effective quantum impurity problem. In addition to normal-state and magnetic phases we also allow for the occurrence of a superconducting phase. In the normal phase we observe a very sensitive dependence of the low-energy scale on the conduction-electron interaction. We discuss the dependence of the superconducting transition on the interplay between attractive interaction and Kondo exchange.Comment: Submitted to ICM 2009 Conference Proceeding

Conserving approximations in direct perturbation theory: new semianalytical impurity solvers and their application to general lattice problems

For the treatment of interacting electrons in crystal lattices approximations based on the picture of effective sites, coupled in a self-consistent fashion, have proven very useful. Particularly in the presence of strong local correlations, a local approach to the problem, combining a powerful method for the short ranged interactions with the lattice propagation part of the dynamics, determines the quality of results to a large extent. For a considerable time the non crossing approximation (NCA) in direct perturbation theory, an approach originally developed by Keiter for the Anderson impurity model, built a standard for the description of the local dynamics of interacting electrons. In the last couple of years exact methods like the numerical renormalization group (NRG) as pioneered by Wilson, have surpassed this approximation as regarding the description of the low energy regime. We present an improved approximation level of direct perturbation theory for finite Coulomb repulsion U, the crossing approximation one (CA1) and discuss its connections with other generalizations of NCA. CA1 incorporates all processes up to fourth order in the hybridization strength V in a self-consistent skeleton expansion, retaining the full energy dependence of the vertex functions. We reconstruct the local approach to the lattice problem from the point of view of cumulant perturbation theory in a very general way and discuss the proper use of impurity solvers for this purpose. Their reliability can be tested in applications to e.g. the Hubbard model and the Anderson-lattice model. We point out shortcomings of existing impurity solvers and improvements gained with CA1 in this context. This paper is dedicated to the memory of Hellmut Keiter.Comment: 45 pages, 22 figure

Low-energy properties of the Kondo lattice model

We study the zero-temperature properties of the Kondo lattice model within the dynamical mean-field theory. As impurity solver we use the numerical renormalization group. We present results for the paramagnetic case showing the anticipated heavy Fermion physics, including direct evidence for the appearance of a large Fermi surface for antiferromagnetic exchange interaction. Allowing for the formation of a Neel state, we observe at finite doping an antiferromagnetic metal below a critical exchange interaction, which shows a crossover from a local-moment antiferromagnet with a small Fermi surface for weak exchange coupling to a heavy-fermion antiferromagnet with a large Fermi surface for increasing exchange. Including lattice degrees of freedom via an additional Holstein term we observe a significant suppression of the Kondo effect, leading to strongly reduced lowenergy scale. For too large electron-phonon coupling we find a complete collaps of the heavy Fermi liquid and the formation of polarons.Comment: 11 pages, 7 figure

Dynamic susceptibilities of the single impurity Anderson model within an enhanced non-crossing approximation

The single impurity Anderson model (SIAM) is studied within an enhanced non-crossing approximation (ENCA). This method is extended to the calculation of susceptibilities and thoroughly tested, also in order to prepare applications as a building block for the calculation of susceptibilities and phase transitions in correlated lattice systems. A wide range of model parameters, such as impurity occupancy, temperature, local Coulomb repulsion and hybridization strength, are studied. Results for the spin and charge susceptibilities are presented. By comparing the static quantities to exact Bethe ansatz results, it is shown that the description of the magnetic excitations of the impurity within the ENCA is excellent, even in situations with large valence fluctuations or vanishing Coulomb repulsion. The description of the charge susceptibility is quite accurate in situations where the singly occupied ionic configuration is the unperturbed ground state; however, it seems to overestimate charge fluctuations in the asymmetric model at too low temperatures. The dynamic spin excitation spectra is dominated by the Kondo-screening of the impurity spin through the conduction band, i.e. the formation of the local Kondo-singlet. A finite local Coulomb interaction U leads to a drastic reduction of the charge response via processes involving the doubly occupied impurity state. In the asymmetric model, the charge susceptibility is enhanced for excitation energies smaller than the Kondo scale T_K due to the influence of valence fluctuations.Comment: 16 pages, 13 figure

Anomalous Normal-State Properties of High-Tc_c Superconductors -- Intrinsic Properties of Strongly Correlated Electron Systems?

A systematic study of optical and transport properties of the Hubbard model, based on Metzner and Vollhardt's dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one), and also compare qualitatively with many anomalous transport features of the high-T$_c$ cuprates. This anomalous behavior of the normal-state properties is traced to a ``collective single-band Kondo effect,'' in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.Comment: 27 pages, latex, 13 figures, Invited for publication in Advances in Physic

Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models

The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.Comment: 20 pages, 9 figures, accepted to PR

Band Calculation for Ce-compounds on the basis of Dynamical Mean Field Theory

The band calculation scheme for $f$ electron compounds is developed on the basis of the dynamical mean field theory (DMFT) and the LMTO method. The auxiliary impurity problem is solved by a method named as NCA$f^{2}$v', which includes the correct exchange process of the $f^{1} \to f^{2}$ virtual excitation as the vertex correction to the non-crossing approximation (NCA) for the $f^{1} \to f^{0}$ fluctuation. This method leads to the correct magnitude of the Kondo temperature, $T_{\rm K}$, and makes it possible to carry out quantitative DMFT calculation including the crystalline field (CF) and the spin-orbit (SO) splitting of the self-energy. The magnetic excitation spectra are also calculated to estimate $T_{\rm K}$. It is applied to Ce metal and CeSb at T=300 K as the first step. In Ce metal, the hybridization intensity (HI) just below the Fermi energy is reduced in the DMFT band. The photo-emission spectra (PES) have a conspicuous SO side peak, similar to that of experiments. $T_{\rm K}$ is estimated to be about 70 K in $\gamma$-Ce, while to be about 1700 K in $\alpha$-Ce. In CeSb, the double-peak-like structure of PES is reproduced. In addition, $T_{\rm K}$ which is not so low is obtained because HI is enhanced just at the Fermi energy in the DMFT band.Comment: 30pages, 18 figure

Unified description of Fermi and non-Fermi liquid behavior in a conserving slave boson approximation for strongly correlated impurity models

We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the Kondo limit the bound state contributions are unimportant.Comment: 4 pages, Latex, 3 postscript figures included Final version with minor changes in wording, to appear in Phys.Rev.Let

Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation

The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed by introducing an appropriate vertex correction explicitly. Using the same vertex correction, the self-energy is investigated, and it is found that under certain assumptions it reproduces the result of the modified perturbation theory which interpolates the weak and the strong correlation limits.Comment: 5 pages, 7 figures, submitted to J. Phys. Soc. Jp

Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials

We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean field-density functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion which determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.Comment: 5 pages, 3 figures, submitted to PRL on March 29, 2000 New version: 10 pages, 9 figures, forwarded to PRE on October 16, 200