Anomalously localized states in the Anderson model

It is demonstrated that anomalously localized states (ALS) in the Anderson model, being lattice specific, are not related to any of the continuous theories. We identify the spatial structure of ALS on a lattice and calculate their likelihood. Analytical results explain peculiarities in previous numerical simulations.     

Electron correlation effects on Anderson localized states

A theoretical model is presented to investigate the effects of electron correlation on the Anderson localized states, and the spin susceptibility and electronic specific heat are calculated. It is shown tha a remarkable effect of correlation in the intermediate region is to give rise to the Curie type behaviour at low temperatures in the spin susceptibility which otherwise obeys the Pauli law. It is further shown that the correlation effect on the T linear term in the specific heat is very small.     

Narrow band limit of the periodic Anderson model with an interatomic hybridization

We analyze the single-particle part of the periodic Anderson model starting from the atomic representation for band (5d) and localized (4f) orbitals. This system with an interatomic hybridization, is transformed into a two-band structure with an intraatomic mixing between the component bands. The resultant hybridized-band structure has narrow lower band with a singular density of states (DOS) at its upper edge.The importance of this singularity for orbitally degenerate 4f or 5f systems is briefly discussed.     

Phase diagram,correlations,and quantum critical point in the periodic Anderson model

Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.     

Critical transport and anomalously localized states at the Anderson transition

The effect of anomalously localized states (ALS) for electron transport at the critical point of the Anderson transition is numerically investigated for two-dimensional symplectic systems. Defining ALS quantitatively, it is found that a probability of finding ALS at criticality increases with the system size, and saturates in an infinite system. This remarkable feature influences transport properties at criticality.     

Lower subband splitting and superconductivity of 2D Hubbard fermions with strong intersite correlations

The effect of the strong intersite Coulomb correlations on the formation of an electron structure in the Shubin-Vonsowsky model in the regime of strong one-site correlations is studied. The results reveal a split-off band of the Fermi states. The spectral intensity of this band grows with the enhancement of the doping level and is determined by the mean-square fluctuation of occupation numbers. This changes the structure of the electron density of states qualitatively.     

Exact insulating and conducting ground states of a periodic Anderson model in three dimensions

We present a class of exact ground states of a three-dimensional periodic Anderson model at 3/4 filling. Hopping and hybridization of d and f electrons extend over the unit cell of a general Bravais lattice. Employing novel composite operators combined with 55 matching conditions the Hamiltonian is cast into positive semidefinite form. A product wave function in position space allows one to identify stability regions of an insulating and a conducting ground state. The metallic phase is a non-Fermi liquid with one dispersing and one flat band.     

Metal-insulator transitions in the periodic Anderson model

We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime.     

Specific heat for the periodic Anderson model

We have considered the symmetric periodic Anderson model (PAM). The specific heat has been calculated in the approximation which corresponds to the Nagaoka-type decoupling scheme for the case of single impurity. It starts to have a double peak structure with the increase of Coulomb repulsion U in analogy to the results for single impurity Anderson model. We have found that the width of a gap in the density of states around the Fermi energy decreases with the increase of U and vanishes for infinite value of this parameter.     

Valence transition in the periodic Anderson model

A very rich phase diagram has recently been found in CeCu₂Si₂ from high pressure experiments where, in particular, a transition between an intermediate valence configuration and an integral valent heavy fermion state has been observed. We show that such a valence transition can be understood in the framework of the periodic Anderson model. In particular, our results show a breakdown of a mixed-valence state which is accompanied by a drastic change in the f occupation in agreement with experiment. This valence transition can possibly be interpreted as a collapse of the large Fermi surface of the heavy fermion state which incorporates not only the conduction electrons but also the localized f electrons. The theoretical approach used in this paper is based on the novel projector-based renormalization method (PRM). With respect to the periodic Anderson model, the method was before only employed in combination with the basic approximations of the well-known slave-boson mean-field theory. In this paper, the PRM treatment is performed in a more sophisticated manner where both mixed as well as integral valent solutions have been obtained. Furthermore, we argue that the presented PRM approach might be a promising starting point to study the competing interactions in CeCu₂Si₂ and related compounds.     

Magnetism and superconductivity in the extended periodic Anderson model

The Anderson model for a periodic array of magnetic ions has been extended by a BCS like interaction term for the conduction electrons. This extended model is studied by means of a generalized Hartree-Fock approximation. Five coupled self-consistency equations are considered for situations where ferromagnetic, superconducting, coexistent and normal phases can occur. Which of these phases actually are allowed for a given set of parameters strongly depends upon the band structure (especially upon the type of electrons near the Fermi energy). Whereas for the general case the self-consistency equations have to be solved numerically from the beginning, the situation is much simplified for the symmetric Anderson model (E _o=–U/2). Here, analytical results are obtained which explain the stability of the coexistent phase. We also use the symmetric model for an expansion of the Ginzburg-Landau type in the spatially homogeneous magnetic and superconducting order parameters. The onset of superconductivity and ferromagnetic order is well described within this approximation. However, at low temperatures we find drastically different solutions due to the strong temperature dependence of the expansion coefficients of the free energy. Therefore, it is difficult to obtain the correct transition temperatures within this approximation. These difficulties stem from general problems connected with the derivation of a Ginzburg-Landau theory for several order parameters from a microscopic theory.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Anomaly in the band centre of the one-dimensional Anderson model

We calculate the density of states and various characteristic lengths of the one-dimensional Anderson model in the limit of weak disorder. All these quantities show anomalous fluctuations near the band centre. This has already been observed for the density of states in a different model by Gorkov and Dorokhov, and is in close agreement with a Monte-Carlo calculation for the localization length by Czycholl, Kramer and Mac-Kinnon.Based in part on the Staatsexamens-thesis by M.K., April 1981. Supported in part by the Sonderforschungsbereich 123 Stochastic Mathematical Models of the Deutsche Forschungsgemeinschaft     

A non-crossing approximation for the study of intersite correlations

We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a self-consistently embedded periodic cluster of size . It is a fully causal and systematic approximation to the full lattice problem, with corrections in two dimensions. The NCA we develop is a systematic approximation with corrections . The method will be discussed in detail and results for the one-particle properties of the Hubbard model are shown. Near half filling, the spectra display pronounced features including a pseudogap and non-Fermi-liquid behavior due to short-ranged antiferromagnetic correlations. Received 16 June 1999     

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean-field equations are iterated with Anderson mixing. The different methods are tested on the triply periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.     

Exact superconducting ground states of the extended Anderson model

We obtain exact ground states of an extended periodic Anderson model (EPAM) with non-local hybridization and Coulomb repulsion between f and c electrons (Falicov-Kimball term) in one dimension. We show that for a range of parameter values these ground states exhibit composite hole pairing and superconductivity that originate from purely electronic interactions.