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Exact Solution of a 2D Interacting Fermion Model
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
2012 (Engelska)Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 314, nr 1, s. 1-56Artikel i tidskrift (Refereegranskat) Published
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.

Ort, förlag, år, upplaga, sidor
2012. Vol. 314, nr 1, s. 1-56
Nyckelord [en]
Coupled Luttinger Liquids, Arbitrary Dimension, Field Theory, Surface, Bosonization, Renormalization, Behavior, Particle, System, Gas
Nationell ämneskategori
Annan fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-50581DOI: 10.1007/s00220-012-1518-8ISI: 000307271600001Scopus ID: 2-s2.0-84863311171OAI: oai:DiVA.org:kth-50581DiVA, id: diva2:462213
Forskningsfinansiär
Vetenskapsrådet
Anmärkning

QC 20120910. Updated from submitted to published.

Tillgänglig från: 2011-12-06 Skapad: 2011-12-06 Senast uppdaterad: 2017-12-08Bibliografiskt granskad
Ingår i avhandling
1. Fermions in two dimensions and exactly solvable models
Öppna denna publikation i ny flik eller fönster >>Fermions in two dimensions and exactly solvable models
2011 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2011. s. viii, 96
Serie
Trita-FYS, ISSN 0280-316X ; 2011:56
Nyckelord
Bosonization, Exactly solvable models, Hubbard model, Mean field theory, Quantum field theory, Strongly correlated systems
Nationell ämneskategori
Den kondenserade materiens fysik
Identifikatorer
urn:nbn:se:kth:diva-50471 (URN)978-91-7501-174-5 (ISBN)
Disputation
2011-12-16, Svedbergssalen, Roslagstullsbacken 21, AlbaNova, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Anmärkning
QC 20111207Tillgänglig från: 2011-12-07 Skapad: 2011-12-06 Senast uppdaterad: 2011-12-07Bibliografiskt granskad

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