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The Hubbard Model : Its Physics and Mathematical Physics - Dionys Baeriswyl

The Hubbard Model

Its Physics and Mathematical Physics

By: Dionys Baeriswyl (Editor), David K. Campbell (Editor), Jose M.P. Carmelo (Editor), Francisco Guinea (Editor), Enrique Louis (Editor)

Hardcover Published: 30th November 1995
ISBN: 9780306450037
Number Of Pages: 407

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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).

The Hubbard Model: Some Rigorous Results and Open Problemsp. 1
On the Bethe Ansatz Soluble Degenerate Hubbard Modelp. 21
Thermodynamical Properties of the Exactly Solvable 1/r-Hubbard and 1/r-t[actual symbol not reproducible] Modelp. 29
Hierarchy of 1-D Electron Models with Long-Range Interactionp. 39
One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solutionsp. 47
Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetryp. 55
Hidden Symmetry of Strongly Correlated Fermionsp. 63
Symmetries of Strongly Correlated Electronsp. 71
Exact Results on a Supersymmetric Extended Hubbard Modelp. 84
Functional Integrals for Correlated Electronsp. 89
Charge-Spin Separation and Pairing in a Generalized Hubbard Modelp. 103
A Renormalization Procedure for the Hubbard Modelp. 113
New Operator Algebra for the Hubbard Chainp. 117
Exact Results and Conjectures on the Adiabatic Holstein-Hubbard Model at Large Electron-Phonon Couplingp. 125
Ferromagnetism in Correlated Electron Systems: A New Class of Rigorous Criteriap. 145
The Mott Transition in Infinite Dimensions: Old Ideas and Some Surprisesp. 155
The Hubbard Model with Local Disorder in d = Infinityp. 167
The Hubbard Model with Infinite Interaction: Magnetic Propertiesp. 175
The Extended Hubbard Model at Large Interactionp. 185
Drude Weight and f-Sum Rule of the Hubbard Model at Strong Couplingp. 193
The Gutzwiller Projector in the Large U-Hubbard Modelp. 201
Revising the 1/N Expansion for the Slave-Boson Approach within the Functional Integralp. 209
"Infarared Catastrophe:" When Does It Trash Fermi Liquid Theory?p. 217
Two-Particle Scattering and Orthogonality Catastrophe in the Hubbard Modelp. 227
Failure of Fermi Liquid Theory in 2-Dimensions: How to Infer It from Peturbation Theoryp. 237
Conservation Laws in Normal Metals: Luttinger Liquid vs. Fermi Liquidp. 251
Charge-Spin Separation and the Spectral Properties of Luttinger Liquidsp. 263
Non-Fermi Behavior in the Kondo and Heisenberg Modelsp. 273
Luttinger-Liquid Behavior in 2-D: The Variational Approachp. 277
Non-Fermi Liquid Behavior of Electrons in the 2-D Honeycomb Lattice: A Renormalization Group Analysisp. 283
Search for Deviations from Fermi Liquid Behavior in 2-D Repulsive and Attractive Hubbard Modelsp. 287
Hartree-Fock and RPA Studies of the Hubbard Modelp. 295
From One- to Two-Dimensions in the Weak Coupling Limitp. 303
Metal-Insulator Transition in the 2-D Hubbard Model: A Fermionic Linearization Approachp. 307
The Phase Diagram of the One-Dimensional Extended Hubbard Modelp. 315
Quantum-Monte-Carlo Simulations of Correlation Functions for the One-Dimensional Hubbard Modelp. 327
Quantum-Monte-Carlo Studies of One- and Two-Dimensional Hubbard Modelsp. 331
Effect of Disorder on Several Properties of the One-Band Hubbard Model in 2-Dp. 341
The Wavefunction Renormalization Constant for the One- and Two-Band Hubbard Hamiltonians in Two-Dimensionsp. 349
Electron Spectroscopy and Hubbard: Issues and Opportunitiesp. 357
On Electrical Properties of Chalcogenide Glassy Semiconductors in the Framework of Hubbard Model with Negative Correlation Energyp. 373
The Metal Insulator Transition in the Hubbard Modelp. 377
Metal to Insulator Transition in the 2-D Hubbard Model: A Slave-Boson Approachp. 385
The Hubbard Model and Its Application to Conjugated [pi]-Electron Systemsp. 393
Indexp. 401
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306450037
ISBN-10: 0306450038
Series: NATO Science Series B:
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 407
Published: 30th November 1995
Publisher: SPRINGER VERLAG GMBH
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 2.39
Weight (kg): 0.95

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