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Exactly solvable models for 2D correlated fermions | Edwin Langmann
; | Date: |
4 Jun 2002 | Journal: | J.Phys. A37 (2004) 407-424 | Subject: | Strongly Correlated Electrons; Exactly Solvable and Integrable Systems | cond-mat.str-el hep-th nlin.SI | Abstract: | I discuss many-body models for interacting fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: 2D fermions in a constant magnetic field and a particular non-local 4-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra $gl_inftyoplus gl_infty$. There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods. | Source: | arXiv, cond-mat/0206045 | Services: | Forum | Review | PDF | Favorites |
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