Exactly solvable models for 2D correlated fermions

Details Exactly solvable models for 2D correlated fermions Exactly solvable models for 2D correlated fermions

2002-06-04

arxiv.org/abs/cond-mat/0206045v2

J.Phys.A37:407-424,2004

Physics

Condensed Matter

Strongly Correlated Electrons

19 pages; v2 substantially revised; further results added; v1 can be read as summary

Scientific paper

10.1088/0305-4470/37/2/010

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 $\gl_\infty\oplus \gl_\infty$. 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.

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