Phy5670/HubbardModel: Difference between revisions
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History of it <br> | History of it <br> | ||
Utility<br> | Utility<br> | ||
The model referred to as the Hubbard model appeared in the literature for the first time in 1963, in two subsequent independent papers -- the first by Gutzwiller, and the second by Hubbard -- as an attempt to describe in a simplified way the effect of correlations for d-electrons in a transition metals, In deed in the latter case the feature that electrons form a (narrow) delocalized <math>d</math>-band is in competition with the quasi-atomic behavior originated from correlations, which would make plausible an atomic description of the problem. The model hamiltonian <math>H</math> consists of two contributions, | |||
==The One-Dimensional Hubbard Model== | ==The One-Dimensional Hubbard Model== | ||
Revision as of 16:14, 8 December 2010
The Hubbard Model
Introduction
What it is
History of it
Utility
The model referred to as the Hubbard model appeared in the literature for the first time in 1963, in two subsequent independent papers -- the first by Gutzwiller, and the second by Hubbard -- as an attempt to describe in a simplified way the effect of correlations for d-electrons in a transition metals, In deed in the latter case the feature that electrons form a (narrow) delocalized -band is in competition with the quasi-atomic behavior originated from correlations, which would make plausible an atomic description of the problem. The model hamiltonian consists of two contributions,
The One-Dimensional Hubbard Model
Main focus, since cannot be solved exactly in Higher D.
Solution by Bethe Ansatz
Thermodynamic Properties
Higher Dimensions
Short discussion of usefulness of numerical results/methods
Related Physical Systems
Mott Insulators
Ultra-Cold atoms.