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Exactly solvable models for 2D correlated fermions
KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.ORCID iD: 0000-0001-7481-2245
2004 (English)In: Journal of Physics A: Mathematical and General, Vol. 37, no 2, p. 407-423Article in journal (Refereed) 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∞ ⊕ gl∞. 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.

Place, publisher, year, edition, pages
2004. Vol. 37, no 2, p. 407-423
National Category
Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249119DOI: 10.1088/0305-4470/37/2/010ISI: 000188801800011Scopus ID: 2-s2.0-0742288608OAI: oai:DiVA.org:kth-249119DiVA, id: diva2:1303824
Funder
Swedish Research Council
Note

QC 20190515

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-05-15Bibliographically approved

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Langmann, Edwin

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