LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XV: Fifteenth Training Course in the Physics of Strongly Correlated Systems
1419(2011); http://dx.doi.org/10.1063/1.3667323View Description Hide Description
1419(2011); http://dx.doi.org/10.1063/1.3667324View Description Hide Description
Low‐temperature physical properties of d‐ and f‐electron transition‐metal intermetallics are often dominated by strong interactions among the conduction electrons. New developments started with considerations of the stability of magnetic moments in a metallic matrix, first as impurities and later as residing on regular lattice sites of compounds. A special case are compounds where these interactions provoke a transfer of magnetic degrees of freedom to the subsystem of the conduction electrons, resulting in extreme enhancements of the effective mass of these charge carriers and to quantum‐critical behaviour.. Of particular interest is the onset of superconductivity in this type of compounds, with strong indications of unconventional superconducting phases in the vicinity of magnetic order. Evidence for unconventional superconductivity is also obtained from studies of systems close to a metal‐insulator transition. Examples are oxide materials, most spectacularly the Cu oxides exhibiting high‐ superconductivity.
Strong correlations are also met in spin systems of insulating compounds. They are particularly effective in materials with low‐dimensional structure units, such as chains, ladders and planes. At low temperatures such systems, mostly d‐transition metal oxides of different varieties, are often dominated by quantum effects and quantum criticality and provide a rich playground for studies of related phenomena. You may want to print this page and refer to it as a style sample before you begin working on your paper.
1419(2011); http://dx.doi.org/10.1063/1.3667325View Description Hide Description
The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the ground‐state energy or, at finite temperatures, to the free energy of the system as well as to other static physical quantities. Elementary excitations of the system, on the other hand, are described within the language of Green's functions, i.e. time‐ or frequency‐dependent dynamic quantities which give a direct access to the linear response of the system subjected to a weak time‐dependent external perturbation. A typical example is angle‐revolved photoemission spectroscopy which is linked to the single‐electron Green's function. Since usually both, the static as well as the dynamic physical quantities, cannot be obtained exactly for lattice fermion models like the Hubbard model, one has to resort to approximations. Opposed to more ad hoc treatments, variational principles promise to provide consistent and controlled approximations. Here, the Ritz principle and a generalized version of the Ritz principle at finite temperatures for the static case on the one hand and a dynamical variational principle for the single‐electron Green's function or the self‐energy on the other hand are introduced, discussed in detail and compared to each other to show up conceptual similarities and differences. In particular, the construction recipe for non‐perturbative dynamic approximations is taken over from the construction of static mean‐field theory based on the generalized Ritz principle. Within the two different frameworks, it is shown which types of approximations are accessible, and their respective weaknesses and strengths are worked out. Static Hartree‐Fock theory as well as dynamical mean‐field theory are found as the prototypical approximations.
1419(2011); http://dx.doi.org/10.1063/1.3667326View Description Hide Description
I show the symmetries of the compass model and spin transformations making the Hamiltonian block‐diagonal. I present the new form of the Hamiltonian and explain how the diagonal blocks are related by translational symmetry and by the isotropy of interactions. I reveal the hidden symmetry of the lowest‐energy block and resulting identities in four‐point dimer‐dimer correlators. Using exact diagonalization I show that the ground state has classical order with local quantum fluctuation vanishing in a long range and that the energy spectrum consists of discrete and continuous part.
1419(2011); http://dx.doi.org/10.1063/1.3667327View Description Hide Description
In this work we use a Schrieffer‐Wolff transformation in a two‐fold degenerate periodic Anderson lattice to describe the coexistence of Kondo effect and ferromagnetism in some uranium and neptunium compounds. We show that the inclusion of a bandwidth for the f electrons can account for a weak delocalization of 5f electrons. Using a mean field approximation, we show that a maximum of versus can be found when the bandwidth is proportional to
Interplay between strong correlations and electron‐phonon coupling in cuprates: Comparison between different models1419(2011); http://dx.doi.org/10.1063/1.3667328View Description Hide Description
We investigate influence of electron‐phonon coupling on physics of lightly doped cuprates. Using an exact‐diagonalization technique defined over a limited functional space we compare properties of two doped holes propagating in an antiferromagnetic (AFM) background, coupled to quantum phonons in two alternative ways. In the first model phonons interact with hole density via Holstein coupling leading to the t‐J Holstein model, and in the second model lattice vibrations modify the hole hopping in the effective t‐J model. We show that the former lead to stabilization of d‐wave pairing, while in the latter case a state with p‐wave symmetry is favored. The results emphasize a subtle interplay between electronic correlations and lattice vibrations in cuprates as well as the importance of different modeling of e‐ph interaction.