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Aspects of strong correlations in low dimensions

Aspekte starker Korrelationen in niedrigen Dimensionen

  • The challenging intricacies of strongly correlated electronic systems necessitate the use of a variety of complementary theoretical approaches. In this thesis, we analyze two distinct aspects of strong correlations and develop further or adapt suitable techniques. First, we discuss magnetization transport in insulating one-dimensional spin rings described by a Heisenberg model in an inhomogeneous magnetic field. Due to quantum mechanical interference of magnon wave functions, persistent magnetization currents are shown to exist in such a geometry in analogy to persistent charge currents in mesoscopic normal metal rings. The second, longer part is dedicated to a new aspect of the functional renormalization group technique for fermions. By decoupling the interaction via a Hubbard-Stratonovich transformation, we introduce collective bosonic variables from the beginning and analyze the hierarchy of flow equations for the coupled field theory. The possibility of a cutoff in the momentum transfer of the interaction leads to a new flow scheme, which we will refer to as the interaction cutoff scheme. Within this approach, Ward identities for forward scattering problems are conserved at every instant of the flow leading to an exact solution of a whole hierarchy of flow equations. This way the known exact result for the single-particle Green's function of the Tomonaga-Luttinger model is recovered.
  • Diese Dissertation diskutiert in zwei Teilen unterschiedliche Aspekte stark korrelierter Elektronensysteme. Neben der Untersuchung physikalischer Fragestellungen werden dabei Vielteilchenmethoden neu entwickelt und angepasst. Im ersten Teil behandeln wir Magnetisierungstransport in eindimensionalen Spinringen, die durch ein Heisenbergmodell in einem inhomogenen Magnetfeld beschrieben werden. In Analogie zu Ladungsdauerströmen in mesoskopischen normalleitenden Metallringen können in einer solchen Geometrie aufgrund quantenmechanischer Interferenz der Magnon-Wellenfunktionen Spindauerströme auftreten. Der zweite Teil der Arbeit beschäftigt sich mit neuen Aspekten der funktionalen Renormierungsgruppe für Fermionen. Durch eine Entkopplung der Wechselwirkung mittels einer geeigneten Hubbard-Stratonovich-Transformation führen wir kollektive bosonische Felder ein und analysieren die Hierarchie von Flussgleichungen für die gekoppelte Feldtheorie. Die Möglichkeit eines Cutoffs im Impulsübertrag der Wechselwirkung führt zu einer neuen Technik, die wir als "Wechselwirkungs-Fluss" bezeichnen. In diesem Zugang sind Ward-Identitäten für Vorwärtsstreuung zu jedem Zeitpunkt des Renormierungsgruppenflusses gültig, und liefern eine exakte Lösung für eine komplette Hierarchie von Flussgleichungen. Auf diese Weise erhalten wir das bekannte exakte Ergebnis für die Einteilchen Greensche Funktion des Tomonaga-Luttinger Modells.

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Metadaten
Author:Florian SchützGND
URN:urn:nbn:de:hebis:30-16018
Referee:Peter KopietzORCiDGND, Roser ValentíORCiDGND
Advisor:Peter Kopietz
Document Type:Doctoral Thesis
Language:English
Year of Completion:2005
Year of first Publication:2005
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2005/09/07
Release Date:2005/10/14
GND Keyword:Magnetoelektronik; Renormierungsgruppe; Heisenberg-Modell; Fermionensystem; Eindimensionaler Leiter
Page Number:178
HeBIS-PPN:133486435
Institutes:Physik / Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
PACS-Classification:70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 71.00.00 Electronic structure of bulk materials (see section 73 for electronic structure of surfaces, interfaces, low-dimensional structures, and nanomaterials; for electronic structure of superconductors, see 74.25.Jb) / 71.10.-w Theories and models of many-electron systems / 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems
70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 71.00.00 Electronic structure of bulk materials (see section 73 for electronic structure of surfaces, interfaces, low-dimensional structures, and nanomaterials; for electronic structure of superconductors, see 74.25.Jb) / 71.10.-w Theories and models of many-electron systems / 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) (for anyon mechanism in superconductors, see 74.20.Mn)
70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 73.00.00 Electronic structure and electrical properties of surfaces, interfaces, thin films, and low-dimensional structures (for electronic structure and electrical properties of superconducting films and low-dimensional structures, see 74.78.-w; for computational / 73.23.-b Electronic transport in mesoscopic systems / 73.23.Ra Persistent currents
70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 75.00.00 Magnetic properties and materials (for magnetic properties of quantum solids, see 67.80.dk; for magnetic properties related to treatment conditions, see 81.40.Rs; for magnetic properties of superconductors, see 74.25.Ha; for magnetic properties of rocks a / 75.10.-b General theory and models of magnetic ordering (see also 05.50.+q Lattice theory and statistics) / 75.10.Pq Spin chain models
70.00.00 CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES / 75.00.00 Magnetic properties and materials (for magnetic properties of quantum solids, see 67.80.dk; for magnetic properties related to treatment conditions, see 81.40.Rs; for magnetic properties of superconductors, see 74.25.Ha; for magnetic properties of rocks a / 75.30.-m Intrinsic properties of magnetically ordered materials (for critical point effects, see 75.40.-s) / 75.30.Ds Spin waves (for spin-wave resonance, see 76.50.+g)
Licence (German):License LogoDeutsches Urheberrecht