LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS IX: Ninth Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors
789(2005); http://dx.doi.org/10.1063/1.2080347View Description Hide Description
This course has a dual purpose. First we review the successes of the weak‐coupling BCS theory in describing new classes of superconductors discovered since 1979. They include the heavy‐fermion superconductors, organic superconductors, high‐Tc cuprate superconductors, Sr2RuO4 etc. Second, we present the quasiclassical approximation introduced by Volovik, which we extend to describe the thermodynamics and the thermal conductivity of the vortex state in nodal superconductors. This approach provides the most powerful tool in identifying the symmetry of the energy gap function Δ(k) in these new superconductors.
789(2005); http://dx.doi.org/10.1063/1.2080348View Description Hide Description
Since the discovery of high T c superconductors in cuprate oxides, physics of highly correlated electron systems has become one of the central issues in condensed matter physics. We can find many examples of highly correlated particle systems not only in electron systems, such as high T c superconductors and transition metal oxides, but also in bosonic systems, such as alkaline atomic gases in an optical lattice and mesoscopic Josephson junction arrays. In this lecture, we illustrate several models of highly correlated particle systems of fermionic and bosonic systems, and clarify common features of these systems. Then theoretical approaches to analyze these systems will be reviewed; special emphasis is on the composite operator method, which has been developed by the present author and the Salerno group.
789(2005); http://dx.doi.org/10.1063/1.2080349View Description Hide Description
In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many‐body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson’s Numerical Renormalization Group (NRG) and White’s Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low‐dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.
789(2005); http://dx.doi.org/10.1063/1.2080350View Description Hide Description
This lecture gives a basic introduction into some aspects of the unconventional superconductivity. First we analyze the conditions to realize unconventional superconductivity in strongly correlated electron systems. Then an introduction of the generalized BCS theory is given and several key properties of unconventional pairing states are discussed. The phenomenological treatment based on the Ginzburg‐Landau formulations provides a view on unconventional superconductivity based on the concept of spontaneous symmetry breaking. Finally some aspects of two examples of unconventional superconductors will be discussed: high‐temperature superconductivity and spin‐triplet superconductivity in Sr2RuO4.
789(2005); http://dx.doi.org/10.1063/1.2080351View Description Hide Description
The periodic Anderson model at arbitrary value of on‐site Coulomb repulsion is studied by the generating functional approach. For the Green’s function of the localized d‐electrons exact equation with variational derivatives with respect to fluctuating fields is derived. It coincides with the one for the Hubbard model if hopping matrix element tij are replaced by the effective ones Δ ij (ω), that depends on frequency and is proportional of the hybridization parameter squared. It is shown that the first order correction with respect to Δ ij (ω) for the terminal part of the Green’s function contains a singular term originating from interaction of d‐electrons with spin fluctuations. Dynamical susceptibility of these fluctuations is calculated in the hydrodynamic limit.
789(2005); http://dx.doi.org/10.1063/1.2080352View Description Hide Description
We consider the problem of the competition and coexistence of singlet superconductivity and itinerant ferromagnetism in a system where the two orders are confined in different layers. The consequences of the charge transfer and the spin exchange between the subsystems are investigated with the aim to extract the region of parameters where a coexistence state is allowed. The results are discussed in the context of layered materials where the coexisting superconductivity and ferromagnetism are due to different electrons, like in the rutheno‐cuprate GdSr2Ru2 Cu 2O8 compound. An analysis of the case where non‐uniform superconductivity may occur is also presented.
789(2005); http://dx.doi.org/10.1063/1.2080353View Description Hide Description
The level of current understanding of the physics of time‐dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one‐dimensional systems. We describe recent developments in the construction of numerical schemes for general (one‐dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest‐neighbor‐interaction and investigate their accuracy by comparing with exact results.
789(2005); http://dx.doi.org/10.1063/1.2080354View Description Hide Description
We give a straightforward generalization of the Ginzburg‐Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb‐Ramond field. While the standard properties of superconductors are recovered for temperatures not very far from the critical one, we predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity. A physical scenario behind the model proposed, which can be directly tested by experiments, is envisaged.
789(2005); http://dx.doi.org/10.1063/1.2080355View Description Hide Description
We study the behaviour of the density functional theory for superconductors (SCDFT) for two cases: 1) the Coulomb part of the condensation energy (E c ) of a homogeneous electron gas under pairing potential with high angular momentum, and 2) the Tc of niobium under pressure.
In the first case, we treat the electronic correlations at the random phase approximation (RPA) level and we do not find superconductivity for densities with rs up to 9, and only a very weak negative value of E c for f‐waves and higher angular momentum when rs =10.
In the second case, low and high pressure anomalies and the absolute values of Tc are reproduced quite well by the linearized SCDFT gap equation (with a Thomas‐Fermi screening of Coulomb interactions and phonons treated within the Migdal’s theorem). In contrast, the critical temperatures of Nb under pressure obtained from the linearized Eliashberg equation are largely overestimated, even when spin‐fluctuations are included.
789(2005); http://dx.doi.org/10.1063/1.2080356View Description Hide Description
A better understanding of the electronic structure of correlated electron materials, such as transition metal oxides, sulfides, and phosphides, may be realized by improving the energy resolution for Resonant Inelastic X‐ray Spectroscopy (RIXS). Current models based on the interplay between on‐site Coulomb interaction, charge‐transfer energy, and overlap of energy bands require a quantitative knowledge of location and dispersion of electronic energy levels near the Fermi level with a resolution better that the existing spectrometers, which vary between 100 meV and 500 meV in the energy range of 5–10 keV. Here, we propose a new spectrometer based on a back‐reflecting sapphire analyzer that will improve the energy resolution to 30 meV for Fe, Ni, Cu, and Zn K‐absorption‐edge RIXS studies.