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  • 1.
    de Woul, Jonas
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Fermions in two dimensions and exactly solvable models2011Doctoral 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.

  • 2.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lundholm, Douglas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge2011In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 1, p. 031-Article in journal (Refereed)
    Abstract [en]

    The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.

  • 3.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lundholm, Douglas
    Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
    Sundin, Martin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A dynamical symmetry for supermembranes2011In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 3, no 134Article in journal (Refereed)
    Abstract [en]

    A dynamical symmetry for supersymmetric extended objects is given.

  • 4.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Exact Solution of a 2D Interacting Fermion Model2012In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 314, no 1, p. 1-56Article in journal (Refereed)
    Abstract [en]

    We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.

  • 5.
    De Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Fermions in two dimensions, bosonization, and exactly solvable models2012In: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 26, no 22, p. 1244005-Article, review/survey (Refereed)
    Abstract [en]

    We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square lattice. We review recent work on a specific relation between a variant of Mattis' model and such a lattice fermion system, as well as the exact solution of this model. The background for this work includes well-established results for one-dimensional systems and the high-T c problem. We also mention exactly solvable extensions of Mattis' model.

  • 6.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge invariance, correlated fermions, and Meissner effect in 2+1 dimensionsArticle in journal (Other academic)
    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.

  • 7.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge Invariance, Correlated Fermions, and Photon Mass in 2+1 Dimensions2014In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 154, no 3, p. 877-894Article in journal (Refereed)
    Abstract [en]

    We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in two dimensional continuum space; this system has two dimensional character due to density-density interactions and due to a coupling to dynamical photons propagating in the continuous embedding space. We argue that this model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. Our results include the following: after non-trivial renormalizations of the coupling parameters, the model remains well-defined in the quantum field theory limit as the grid of lines becomes a continuum; the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model; the exact excitation spectrum of the model has two gapped and one gapless mode.

  • 8.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Partial continuum limit of the 2D Hubbard modelArticle in journal (Other academic)
  • 9.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Partially Gapped Fermions in 2D2010In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 139, no 6, p. 1033-1065Article in journal (Refereed)
    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.

  • 10.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Merle, Alexander
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Ohlsson, Tommy
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Particle Physics.
    Establishing analogies between the physics of extra dimensions and carbon nanotubes2012In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 714, no 1, p. 44-47Article in journal (Refereed)
    Abstract [en]

    We point out a conceptual analogy between the physics of extra spatial dimensions and the physics of carbon nanotubes which arises for principle reasons, although the corresponding energy scales are at least ten orders of magnitude apart. For low energies, one can apply the Kaluza-Klein description to both types of systems, leading to two completely different but consistent interpretations of the underlying physics. In particular, we discuss in detail the Kaluza-Klein description of armchair and zig-zag carbon nanotubes. Furthermore, we describe how certain experimental results for carbon nanotubes could be re-interpreted in terms of the Kaluza-Klein description. Finally, we present ideas for new measurements that could allow to probe concepts of models with extra spatial dimensions in table-top experiments, providing further links between condensed matter and particle physics.

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