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Gauge invariance, correlated fermions, and Meissner effect in 2+1 dimensions
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
(English)Article in journal (Other academic) Submitted
Abstract [en]

We present a 2+1 dimensional quantum gauge theory model with correlated fermions that is exactly solvable by bosonization. This model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. We show that the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model. Moreover, the exact excitation spectrum of the model has two gapped and one gapless mode. We also compute the magnetic field induced by an external current and show that there is a Meissner effect. We find that the transverse photons have significant effects on the low-energy properties of the model even if the fermion-photon coupling is small.

National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-50645OAI: oai:DiVA.org:kth-50645DiVA: diva2:462343
Note
QS 2011 QS 20120326Available from: 2011-12-07 Created: 2011-12-07 Last updated: 2012-03-26Bibliographically approved
In thesis
1. Fermions in two dimensions and exactly solvable models
Open this publication in new window or tab >>Fermions in two dimensions and exactly solvable models
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.
Series
Trita-FYS, ISSN 0280-316X ; 2011:56
Keyword
Bosonization, Exactly solvable models, Hubbard model, Mean field theory, Quantum field theory, Strongly correlated systems
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-50471 (URN)978-91-7501-174-5 (ISBN)
Public defence
2011-12-16, Svedbergssalen, Roslagstullsbacken 21, AlbaNova, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20111207Available from: 2011-12-07 Created: 2011-12-06 Last updated: 2011-12-07Bibliographically approved

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