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Breakdown and absence of quasiparticles in Kitaev’s models

  • This thesis has two main parts. The first part is based on our publication [1], where we use perturbation theory to calculate decay rates of magnons in the Kitaev-Heisenberg-Γ (KHΓ) model. This model describes the magnetic properties of the material α-RuCl 3 , which is a candidate for a Kitaev spin liquid. Our motivation is to validate a previous calculation from Ref. [2]. In this thesis, we map out the classical phase diagram of the KHΓ model. We use the Holstein-Primakoff transformation and the 1/S expansion to describe the low temperature dynamics of the Kitaev-Heisenberg-Γ model in the experimentally relevant zigzag phase by spin waves. By parametrizing the spin waves in terms of hermitian fields, we find a special parameter region within the KHΓ model where the analytical expressions simplify. This enables us to construct the Bogoliubov transformation analytically. For a representative point in the special parameter region, we use these results to numerically calculate the magnon damping, which is to leading order caused by the decay of single magnons into two. We also calculate the dynamical structure factor of the magnons. The second part of this thesis is based on our publication [3], where we use the functional renormalization group to analyze a discontinuous quantum phase transition towards a non-Fermi liquid phase in the Sachdev-Ye-Kitaev (SYK) model. In this thesis, we perform a disorder average over the random interactions in the SYK model. We argue that in the thermodynamic limit, the average renormalization group (RG) flow of the SYK model is identical to the RG flow of an effective disorder averaged model. Using the functional RG, we find a fixed point describing the discontinuous phase transition to the non-Fermi liquid phase at zero temperature. Surprisingly, we find a finite anomalous dimension of the fermions, which indicates critical fluctuations and is unusual for a discontinuous transition. We also determine the RG flow at zero temperature, and relate it to the phase diagram known from the literature.

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Metadaten
Verfasserangaben:Roman Louis SmitORCiDGND
URN:urn:nbn:de:hebis:30:3-714729
DOI:https://doi.org/10.21248/gups.71472
Verlagsort:Frankfurt am Main
Gutachter*in:Peter KopietzORCiDGND, Roser ValentiORCiDGND
Betreuer:Peter Kopietz
Dokumentart:Dissertation
Sprache:Englisch
Datum der Veröffentlichung (online):09.01.2023
Jahr der Erstveröffentlichung:2022
Veröffentlichende Institution:Universitätsbibliothek Johann Christian Senckenberg
Titel verleihende Institution:Johann Wolfgang Goethe-Universität
Datum der Abschlussprüfung:19.12.2022
Datum der Freischaltung:20.01.2023
Freies Schlagwort / Tag:Functional Renormalization Group; Kitaev model; Magnons; SYK model; Spinwaves
Seitenzahl:133
HeBIS-PPN:503804266
Institute:Physik
DDC-Klassifikation:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Sammlungen:Universitätspublikationen
Lizenz (Deutsch):License LogoDeutsches Urheberrecht