Fermions in two dimensions and exactly solvable models
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
This Ph.D. thesis in mathematical physics concerns systems of interacting fermions with strong correlations. For these systems the physical properties can only be described in terms of the collective behavior of the fermions. Moreover, they are often characterized by a close competition between fermion localization versus delocalization, which can result in complex and exotic physical phenomena.
Strongly correlated fermion systems are usually modelled by many-body Hamiltonians for which the kinetic- and interaction energy have the same order of magnitude. This makes them challenging to study as the application of conventional computational methods, like mean field- or perturbation theory, often gives unreliable results. Of particular interest are Hubbard-type models, which provide minimal descriptions of strongly correlated fermions. The research of this thesis focuses on such models defined on two-dimensional square lattices. One motivation for this is the so-called high-Tc problem of the cuprate superconductors.
A main hypothesis is that there exists an underlying Fermi surface with nearly flat parts, i.e. regions where the surface is straight. It is shown that a particular continuum limit of the lattice system leads to an effective model amenable to computations. This limit is partial in that it only involves fermion degrees of freedom near the flat parts. The result is an effective quantum field theory that is analyzed using constructive bosonization methods. Various exactly solvable models of interacting fermions in two spatial dimensions are also derived and studied.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. , viii, 96 p.
Trita-FYS, ISSN 0280-316X ; 2011:56
Bosonization, Exactly solvable models, Hubbard model, Mean field theory, Quantum field theory, Strongly correlated systems
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:kth:diva-50471ISBN: 978-91-7501-174-5OAI: oai:DiVA.org:kth-50471DiVA: diva2:462009
2011-12-16, Svedbergssalen, Roslagstullsbacken 21, AlbaNova, Stockholm, 10:00 (English)
Essler, Fabian, Professor
Langmann, Edwin, Professor
QC 201112072011-12-072011-12-062011-12-07Bibliographically approved
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