U-perturbation treatment of heavy fermion systems

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toE _f andE _f +U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (E _f baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleT _K. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleT _coh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.E _f andE _f +U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsE _f andE _f +U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.     

Coulomb repulsion versus Hubbard repulsion in a disordered chain

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. The system size L (in units of the lattice spacing) is of the order of the one particle localization length and the energies are taken near the band center. In the two cases, the limits of weak and strong interactions are characterized by uncorrelated energy levels and are separated by a crossover regime where the states are more extended and the spectra more rigid. U denoting the interaction strength and t the kinetic energy scale, the crossovers take place for interaction energy to kinetic energy ratios U/t and U/(2tL) of order one, for Hubbard and Coulomb repulsions respectively. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. The interaction matrix elements are studied to explain this difference. Received 21 March 2000 and Received in final form 5 February 2001     

CeO2的电子结构，光学和晶格动力学性质：第一性原理研究

基于考虑了Ce-4f电子间的库仑作用U和交换作用J的LDA+U方案,应用第一性原理计算系统研究了CeO₂的电子结构,光学和晶格动力学性质.电荷密度和电子局域函数的分布特征表明,CeO₂是属于共价键的绝缘体.介电常数、玻恩有效电荷张量和声子色散曲线的计算值和相应的实验结果符合得比较好. 关键词： 电子结构 光学性质 晶格动力学 第一性原理计算     

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Phase transitions in the generalized spin-one-half Falicov–Kimball model in two dimensions

The extrapolation of small-cluster exact-diagonalisation calculations and the Monte-Carlo method is used to study the spin-one-half Falicov–Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction (U _ff ) between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave (CDW) phase and the spin-density-wave (SDW) phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The critical temperature T _c for a transition from the low-temperature ordered phases to the high-temperature disordered phase is calculated numerically for various values of J and U _ff .     

Triplet <Emphasis Type="Italic">p</Emphasis>-wave superconductivity in the low-density extended hubbard model with Coulomb repulsion

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n _el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.     

Electronic structures and mechanical properties of uranium monocarbide from first-principles and calculations

The electronic structure, elastic constants, Poisson's ratio, and phonon dispersion curves of UC have been systematically investigated from the first-principles calculations by the projector-augmented-wave (PAW) method. In order to describe precisely the strong on-site Coulomb repulsion among the localized U 5f electrons, we adopt the local density approximation (LDA)+U and generalized gradient approximation (GGA)+U formalisms for the exchange correlation term. We systematically study how the electronic properties and elastic constants of UC are affected by the different choice of U as well as the exchange-correlation potential. We show that by choosing an appropriate Hubbard U parameter within the GGA+U approach, most of our calculated results are in good agreement with the experimental data. Therefore, the results obtained by the GGA+U with effective Hubbard parameter U chosen around 3 eV for UC are considered to be reasonable.     

Spectral densities of response functions for the O(3) symmetric Anderson and two channel Kondo models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln divergence found in the low frequency behaviour of the T=0 dynamic susceptibility. Received 29 January 1999     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000