Exactly solvable models for 2D correlated fermions
| dc.creator | Langmann, Edwin | |
| dc.date | 2002-06-04 | |
| dc.date | 2003-06-06 | |
| dc.date.accessioned | 2026-07-07T10:48:05Z | |
| dc.date.available | 2026-07-07T10:48:05Z | |
| dc.description | 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. | |
| dc.description | 19 pages; v2 substantially revised; further results added; v1 can be read as summary | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0206045 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0206045 | |
| dc.identifier | J.Phys.A37:407-424,2004 | |
| dc.identifier | doi:10.1088/0305-4470/37/2/010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/183757 | |
| dc.subject | Strongly Correlated Electrons | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Exactly solvable models for 2D correlated fermions | |
| dc.type | text |