The Hubbard Model
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The Hubbard Model: Its Physics and Mathematical Physics

The Hubbard Model: Its Physics and Mathematical Physics

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About the Book

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).

Table of Contents:
Solvable Models, Rigorous Results, and Advances in Formalism.- The Hubbard Model: Some Rigorous Results and Open Problems.- On the Bethe Ansatz Soluble Degenerate Hubbard Model.- Thermodynamical Properties of the Exactly Solvable 1/r-Hubbard and 1/r-tJ Model.- Hierarchy of 1-D Electron Models with Long-Range Interaction.- One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solutions.- Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetry.- Hidden Symmetry of Strongly Correlated Fermions.- Symmetries of Strongly Correlated Electrons.- Exact Results on a Supersymmetric Extended Hubbard Model.- Functional Integrals for Correlated Electrons.- Charge-Spin Separation and Pairing in a Generalized Hubbard Model.- A Renormalization Procedure for the Hubbard Model.- New Operator Algebra for the Hubbard Chain.- Exact Results and Conjectures on the Adiabatic Holstein-Hubbard Model at Large Electron-Phonon Coupling.- Ferromagnetism in Correlated Electron Systems: A New Class of Rigorous Criteria.- Infinite in All Directions: Large Coupling, High Dimensions, and Many Components.- The Mott Transition in Infinite Dimensions: Old Ideas and Some Surprises.- The Hubbard Model with Local Disorder in d = Infinity.- The Hubbard Model with Infinite Interaction: Magnetic Properties.- The Extended Hubbard Model at Large Interaction.- Drude Weight and f-Sum Rule of the Hubbard Model at Strong Coupling.- The Gutzwiller Projector in the Large U-Hubbard Model.- Revising the 1/N Expansion for the Slave-Boson Approach within the Functional Integral.- Fermi Liquid versus Luttinger Liquid.- “Infarared Catastrophe:” When Does It Trash Fermi Liquid Theory?.- Two-Particle Scattering and Orthogonality Catastrophe in the HubbardModel.- Failure of Fermi Liquid Theory in 2-Dimensions: How to Infer it from Peturbation Theory.- Conservation Laws in Normal Metals: Luttinger Liquid vs. Fermi Liquid.- Charge-Spin Separation and the Spectral Properties of Luttinger Liquids.- Non-Fermi Behavior in the Kondo and Heisenberg Models.- Luttinger-Liquid Behavior in 2-D: The Variational Approach.- Non-Fermi Liquid Behavior of Electrons in the 2-D Honeycomb Lattice: A Renormalization Group Analysis.- Search for Deviations from Fermi Liquid Behavior in 2-D Repulsive and Attractive Hubbard Models.- Perturbative, Mean Field, Variational, and Numerical Studies.- Hartree-Fock and RPA Studies of the Hubbard Model.- From One- to Two-Dimensions in the Weak Coupling Limit.- Metal-Insulator Transition in the 2-D Hubbard Model: A Fermionic Linearization Approach.- The Phase Diagram of the One-Dimensional Extended Hubbard Model.- Quantum-Monte-Carlo Simulations of Correlation Functions for the One-Dimensional Hubbard Model.- Quantum-Monte-Carlo Studies of One- and Two-Dimensional Hubbard Models.- Effect of Disorder on Several Properties of the One-Band Hubbard Model in 2-D.- The Wavefunction Renormalization Constant for the One- and Two-Band Hubbard Hamiltonians in Two-Dimensions.- Experiments and Physical Applications.- Electron Spectroscopy and Hubbard: Issues and Opportunities.- On Electrical Properties of Chalcogenide Glassy Semiconductors in the Framework of Hubbard Model with Negative Correlation Energy.- The Metal Insulator Transition in the Hubbard Model.- Metal to Insulator Transition in the 2-D Hubbard Model: A Slave-Boson Approach.- The Hubbard Model and Its Application to Conjugated ?-Electron Systems.


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Product Details
  • ISBN-13: 9780306450037
  • Publisher: Springer Science+Business Media
  • Publisher Imprint: Kluwer Academic/Plenum Publishers
  • Height: 254 mm
  • No of Pages: 407
  • Sub Title: Its Physics and Mathematical Physics
  • ISBN-10: 0306450038
  • Publisher Date: 30 Nov 1995
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Width: 178 mm


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