LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS VI: Sixth Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors
Introduction to Renormalization Group and Ward Identities in Critical Phenomena and in Fermi and Bose Liquids629(2002); http://dx.doi.org/10.1063/1.1509141View Description Hide Description
We review some of the main applications of the renormalization‐group technique in condensed matter physics. The first relevant example is the description of critical phenomena. Here perturbation theory is affected by singularities, which are a consequence of the long‐ranged character of the dominant fluctuations when approaching criticality. The use of renormalization group allows to sum up these singularities into a power‐law behavior of the physical quantities, which is experimentally observed near a continuous phase transition. The second example is provided by the description of the physical properties of interacting Fermi and Bose systems. Here perturbation theory is affected by infrared divergences within stable liquid phases, due to the presence of massless excitations, in reduced dimensionality. However, the condition of stability of the system implies exact cancellations among the singular contributions, controlled by additional Ward identities, which must be considered besides the standard Ward identities related to the conservation of the total particle and spin density. The combined use of renormalization group and these new Ward identities allows for the closure of the renormalization‐group equations, leading to the description of the asymptotic behavior of the system at low energies.
629(2002); http://dx.doi.org/10.1063/1.1509142View Description Hide Description
This set of lectures describes the physics of moment formation, the basic physics of the Kondo effect and the development of a coherent heavy electron fluid in the dense Kondo lattice. The last lecture discusses the open problem of quantum criticality in heavy electron systems.
629(2002); http://dx.doi.org/10.1063/1.1509143View Description Hide Description
Lectures deal with the theory of electronic transport, in particular with the electrical conductivity, in systems dominated by strong electron ‐ electron repulsion. The concept of charge stiffness is introduced to distinguish conductors and insulators at T = 0, but as well usual resistors, possible ideal conductors and ideal insulators at finite temperature. It is shown that the latter singular transport appears in many integrable systems of interacting fermions, the evidence coming from the relation with level dynamics, from the existence of conserved quantities as well as from numerical studies and exact results. Then, exact duagonalization approaches for the calculation of static and dynamical quantities in small correlated systems are described, with the emphasis on the finite‐temperature Lanczos method applicable to transport quantities. Finally, anomalous dynamical conductivity within the planar single‐band model is discussed in relation with experiments on cuprates.
629(2002); http://dx.doi.org/10.1063/1.1509144View Description Hide Description
An introductory survey of the theoretical ideas and calculations and experimental results which depart from Landau Fermi liquids is presented. The common themes and possible routes to the singularities leading to breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of singular or Non Fermi‐liquids include models of impurities in metals with special symmetries and one‐dimensional interacting fermions. A review of these is followed by a discussion of singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low energy collective fluctuations, gauge fields, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two dimensional metallic state.
629(2002); http://dx.doi.org/10.1063/1.1509145View Description Hide Description
The de Haas‐van Alphen‐frequencies as well as the effective masses for a magnetic field parallel to the crystallographic c‐axis are calculated within the local spin density approximation (LSDA) for MgB2 and TaB2. In addition, we analyze the plasma frequencies computed for each Fermi surface sheet. We find a large anisotropy of Fermi velocities in MgB2 in difference to the nearly isotropic behavior in TaB2. We compare calculations performed within the relativistic non‐full potential augmented‐spherical‐wave (ASW) scheme and the scalar‐relativistic full potential local orbital (FPLO) scheme. A significant dependence for small cross sections on the bandstructure method is found. The comparison with the first available experimental de Haas‐van Alphen‐data by Yelland et al. (Ref. 19) shows deviations from the electronic structure calculated within both L(S)DA approaches although the cross section predicted by FPLO are closer to the experimental data. The elucidation of the relevant many‐body effects beyond the standard LDA is considered as a possible key problem to understand the superconductivity in MgB2.
629(2002); http://dx.doi.org/10.1063/1.1509146View Description Hide Description
The spin and orbital phase diagram for perovskite manganites La1−x (Ca,Sr) x MnO3 is numerically calculated as a function of hole concentration by using t‐J spin‐orbital model and adopting the slave‐fermion formalism. The superexchange and double exchange interactions compete with each other and the system demonstrates the highly frustrated behavior. It is shown that the experimentally observed isotropic magnon dispersion in the metallic ferromagnetic phase cannot be reproduced within the slave‐fermion approach.
A combined exact diagonalization ‐ ab initio study of the metallicity and electron localization in nanoscopic systems629(2002); http://dx.doi.org/10.1063/1.1509147View Description Hide Description
We present our new method of approach to the interacting electron systems combining the exact diagonalization of the Hamiltonian in the Fock space (including all hopping integrals and all two‐site interactions) with an ab initio optimization of the single particle (Wannier) functions in the resultant ground state. Such a procedure is applied to the analysis of the electron localization in nanoscopic chains containing up to N = 12 atoms. Electrons are essentially localized for the interatomic distance R > 2.2 Å. The statistical distribution evolves from the Fermi‐liquid limit (at R ∼ 1 − 2 Å) to continuous momentum distribution for R > 2.2 Å. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. Futher applications of our method are listed at the end.
629(2002); http://dx.doi.org/10.1063/1.1509148View Description Hide Description
We present a concise introduction to a new spinwave expansion scheme for magnetically ordered Kondo lattice models. This is motivated by consideration of the ferromagnetically ordered phase of the “double exchange” system La1−x Ca x MnO3. A brief overview is given of the consequences of quantum and thermal fluctuation effects for the magnetic properties of the double exchange ferromagnet.
629(2002); http://dx.doi.org/10.1063/1.1509149View Description Hide Description
The newly‐discovered clathrates Ba6 Ge 25 and its relatives consist of a rigidG ermanium framework, in which Barium or other metallic atoms are trapped. These ‘guest’ atoms can ‘rattle’ freely in the oversized cages at high temperature. In Ba6 Ge 25, some of Ba atoms aref rozen into the split positions randomly below 200 K. This structural phase transition results in a two‐step resistivity jump from metallic behavior to semiconductor‐like behavior characterized by a mean free path of 3Å. Surprisingly, a BCS‐like superconducting transition occursa t Tc ≈ 0.24 K in such a ‘bad metal’. By applying hydrostatic pressure, the structural phase transition is suppressed but Tc increases drastically. Tc reaches a maximum value of 3.85K at a critical pressure pc ≈ 2.8 GPa, where the structural distortion is completely suppressed and the system exhibits metallic behavior over the whole temperature range. Higher pressures lead to a slight decrease of Tc . On replacing 1/3 of the Ba atoms with Na, no structural phase transition iso bserved and the compound displays a similar behavior to Ba6 Ge 25 above pc , with Tc ≈ 1.05 K at ambient pressure. The relationship between the superconductivity and the structural phase transition is briefly discussed.