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Exactly solvable models for 2D interacting fermions
KTH, Tidigare Institutioner, Fysik.
2004 (Engelska)Ingår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 2, s. 407-423Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl(infinity) circle plus gl(infinity). 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.

Ort, förlag, år, upplaga, sidor
2004. Vol. 37, nr 2, s. 407-423
Nyckelord [en]
noncommutative field-theory, grains, spaces
Nationell ämneskategori
Fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-23150DOI: 10.1088/0305-4470/37/2/010ISI: 000188801800011Scopus ID: 2-s2.0-0742288608OAI: oai:DiVA.org:kth-23150DiVA, id: diva2:341848
Anmärkning
QC 20100525 QC 20111031Tillgänglig från: 2010-08-10 Skapad: 2010-08-10 Senast uppdaterad: 2017-12-12Bibliografiskt granskad

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