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Partially Gapped Fermions in 2D
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2010 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 139, no 6, 1033-1065 p.Article in journal (Refereed) Published
Abstract [en]

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.

Place, publisher, year, edition, pages
2010. Vol. 139, no 6, 1033-1065 p.
Keyword [en]
2D lattice fermion systems, Phase diagrams, Mean field theory
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-27875DOI: 10.1007/s10955-010-9971-2ISI: 000277715600007Scopus ID: 2-s2.0-77952412411OAI: oai:DiVA.org:kth-27875DiVA: diva2:385420
Note
QC 20110111Available from: 2011-01-11 Created: 2011-01-03 Last updated: 2017-12-11Bibliographically 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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