The Hubbard Model: Its Physics and Mathematical Physics

ISBN-13: 9781489910448 / Angielski / Miękka / 2013 / 407 str.

Dionys Baeriswyl;David K. Campbell;Jose M. P. Carmelo

Opis

In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret- ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met- als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g., N agoaka's Theorem).

Spis treści

Introduction. Solvable Models, Rigorous Results, and Advances in Formalism: The Hubbard Model: Some Rigorous Results and Open Problems; E.H. Lieb. On the Bethe Ansatz Soluble Degenerate Hubbard Model; H. Frahm, A. Schadschneider. Infinite in all Dimensions: Large Coupling, High Dimensions, Many Components: The Mott Transition in Infinite Dimensions: Old Ideas and Some Surprises; G. KIotliar, M.J. Rozenberg. The Hubbard Model with Infinite Interaction: Magnetic Properties; V.Ya. Krivnov, et al. Fermi Liquid versus Luttinger Liquid: Two Particle Scattering and Orthogonality Catastrophe in the Hubbard Model; W. Metzner. Conservation Laws in Normal Metals: Luttinger Liquid vs. Fermi Liquid C. Di Castro, et al. Perturbative, Mean Field, Variational, and Numerical Studies: Hartree-Fock and RPA Studies of the Hubbard Model; G. Guinea, et al. The Wavefunction Renormalization Constant for the One- and Two-band Hubbard Hamiltonians in Two Dimensions; E. Louis, et al. Experiments and Physical Applications: Electron Spectroscopy and Hubbard: Issues and Opportunities; J.W. Allen, et al. On Electrical Properties of Chalcogenide Glassy Semiconductors in the Framework of Hubbard Model with Negative Correlation Energy; S.D. Savransky. 34 additional articles. Index.