The Hubbard Model: Its Physics and Mathematical PhysicsDionys Baeriswyl, David K. Campbell, Jose M.P. Carmelo, Francisco Guinea, Enrique Louis 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). |
Contents
1 | |
On the Bethe Ansatz Soluble Degenerate Hubbard Model | 21 |
Thermodynamical Properties of the Exactly Solvable 1rHubbard and IrtJ Model | 29 |
Hierarchy of 1D Electron Models with LongRange Interaction | 39 |
OneDimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive | 47 |
Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetry | 55 |
Hidden Symmetry of Strongly Correlated Fermions | 63 |
Symmetries of Strongly Correlated Electrons | 71 |
The Gutzwiller Projector in the Large UHubbard Model | 201 |
Revising the 1N Expansion for the SlaveBoson Approach within the Functional | 209 |
When Does It Trash Fermi Liquid Theory? | 217 |
TwoParticle Scattering and Orthogonality Catastrophe in the Hubbard Model | 227 |
How to Infer It from Peturbation | 237 |
Luttinger Liquid vs Fermi Liquid | 251 |
ChargeSpin Separation and the Spectral Properties of Luttinger Liquids | 263 |
NonFermi Behavior in the Kondo and Heisenberg Models | 273 |
Exact Results on a Supersymmetric Extended Hubbard Model | 81 |
Functional Integrals for Correlated Electrons | 89 |
ChargeSpin Separation and Pairing in a Generalized Hubbard Model | 103 |
A Renormalization Procedure for the Hubbard Model | 113 |
New Operator Algebra for the Hubbard Chain | 117 |
Exact Results and Conjectures on the Adiabatic HolsteinHubbard Model at Large | 125 |
A New Class of Rigorous Criteria | 145 |
Old Ideas and Some Surprises | 155 |
The Hubbard Model with Local Disorder in d Infinity | 167 |
Magnetic Properties | 175 |
The Extended Hubbard Model at Large Interaction | 185 |
Drude Weight and fSum Rule of the Hubbard Model at Strong Coupling | 193 |
HartreeFock and RPA Studies of the Hubbard Model | 295 |
From One to TwoDimensions in the Weak Coupling Limit | 303 |
The Phase Diagram of the OneDimensional Extended Hubbard Model | 315 |
QuantumMonteCarlo Simulations of Correlation Functions for the OneDimensional | 327 |
Effect of Disorder on Several Properties of the OneBand Hubbard Model in 2D | 341 |
The Wavefunction Renormalization Constant for the One and TwoBand Hubbard | 349 |
Issues and Opportunities | 357 |
On Electrical Properties of Chalcogenide Glassy Semiconductors in the Framework | 373 |
A SlaveBoson Approach | 385 |
The Hubbard Model and Its Application to Conjugated лElectron Systems | 393 |
401 | |
Other editions - View all
Common terms and phrases
algebra Anderson antiferromagnetic approximation band behavior Bethe Ansatz bipolaronic boson calculated charge and spin correlation functions corresponding Coulomb density diagonalization dimensional dimensions disorder doping double occupancy effective Hamiltonian electron equation exact excitations Fermi liquid theory Fermi sea Fermi surface fermions ferromagnetism finite fluctuations ground state energy half filling half-filling Hamiltonian Heisenberg hole hopping Hubbard Hamiltonian Hubbard model insulator integral interaction k₁ kinetic energy lattice Lett Lieb limit linear low energy Luttinger liquid magnetic field matrix mean-field metal momentum Mott transition N₁ obtained one-dimensional operators paramagnetic parameter particle perturbation theory phase diagram phase shift phonon Phys physical polaron problem pseudoparticle quantum quasiparticle region renormalization repulsive scattering singlet solution spectral function spectral weight spectrum spinons strong coupling superconductivity symmetry t-J model temperature theorem transition values vector velocities wave function wavefunction zero