Details
| Originalsprache | Englisch |
|---|---|
| Qualifikation | Doctor rerum naturalium |
| Gradverleihende Hochschule | |
| Betreut von |
|
| Datum der Verleihung des Grades | 3 Dez. 2019 |
| Erscheinungsort | Hannover |
| Publikationsstatus | Veröffentlicht - 13 Dez. 2019 |
Abstract
Um den thermodynamischen Grenzwert der Uq[sl(2|1)] 3 ⊗ ̄3-Superspinkette im an- tiferromagnetischen Regime zu untersuchen, analysieren wir die niederenergetischen Anregungen vermöge der exakten Lösung des Models mittels des algebraischen Bethe- Ansatzes. Im isotropen Grenzfall kann die untersuchte Superspinkette zur Modellierung von Plateau-Übergängen in Quanten-Hall-Systemen verwendet werden. Die Definition eines Quasi-Impuls-Operators ermöglicht durch die Einführung einer Quantenzahl für den nicht-kompakten Anteil des Spektrums die Charakterisierung derselben innerhalb des untersuchten Modells. Die entsprechenden Entartungen werden auf dem Gitter durch logarithmische Feinstrukturen aufgehoben. Ausgehend von Extrapolationen unserer Daten für endliche Systemgrößen zeigen wir, dass unter Variationen der Randbedingun- gen von periodisch zu antiperiodisch für die fermionischen Freiheitsgrade Zustände des Kontinuums in diskrete Zustände übergehen und umgekehrt.
Anschließend untersuchen wir den thermodynamischen Grenzwert der q-deformierten osp(3|2) Superspinkette, die im rationalen Limes zur Beschreibung des “intersecting loop”-Modells verwendet werden kann, indem wir die niederenergetischen kritischen Exponenten bestimmen. Wir präsentieren Anhaltspunkte, dass jene aus zwei Coulomb- Gasen unterschiedlicher Radien und den Exponenten der Z(2)-Freiheitsgrade bestehen. Diese Sichtweise wird unterstützt durch die Tatsache, dass das Spektrum des S = 1 XXZ-Heisenbergmodells bei einer bestimmten Anisotropie im Spektrum der Super- spinkette enthalten ist. Insbesondere legen wir dar, dass eine Klasse von Zuständen mit gleicher konformer Dimension, deren Gitterentartungen durch logarithmische Kor- rekturen aufgehoben werden, existiert. Andererseits finden wir ebenfalls Zustände im Spektrum, deren Korrekturen bei endlicher Systemgröße einem Potenzgesetz folgen. Schließlich beobachten wir zwei verschiedene analytische Verhalten des Grundzustandes in Abhängigkeit des Drehwinkels in den Randbedingungen.
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Hannover, 2019. 143 S.
Publikation: Qualifikations-/Studienabschlussarbeit › Dissertation
}
TY - BOOK
T1 - Spin chains and vertex models based on superalgebras
AU - Hobuß, Konstantin
N1 - Doctoral thesis
PY - 2019/12/13
Y1 - 2019/12/13
N2 - The thermodynamic limit of superspin chains can show several intriguing properties, including the emergence of continua of scaling dimensions and the appearance of discrete states when imposing toroidal boundary conditions. Nevertheless, the former’s exhaustive characterization in terms of Conformal Field Theories is still lacking. In order to study the thermodynamic limit of the U_q[sl(2|1)] 3 ⊗ 3̄ superspin chain in the antiferromagnetic regime, we analyze the low lying excitations by means of the model’s exact solution using the Algebraic Bethe Ansatz. In the isotropic limit, this model may be used as a toy model for the description of plateau transitions in Quantum Hall systems. The definition of a quasimomentum operator allows for a characterization of the continua of scaling dimensions, thereby giving rise to a quantum number for the corresponding non-compact component of the spectrum in the thermodynamic limit. The associated degeneracies are lifted on the lattice by logarithmic fine structures. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom, levels from the continuous part of the spectrum flow into discrete levels and vice versa. Investigating the thermodynamic limit of the q-deformed osp(3|2) superspin chain, corresponding to an intersecting loop model in the rational limit, we seek to uncover its low-lying critical exponents. We present evidences that the latter are built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and exponents associated to Z(2) degrees of freedom. This view is supported by the fact that the S = 1 XXZ integrable chain spectrum is present in some of the sectors of the superspin chain at a particular value of the deformation parameter. We find that the fine structure of finite-size effects is very rich for a typical anisotropic spin chain. In fact, we argue on the existence of a family of states with the same conformal dimension whose lattice degeneracies are lifted by logarithmic corrections. On the other hand, we also report on states of the spectrum whose finite-size corrections seem to be governed by a power law behaviour. We finally observe that under toroidal boundary conditions the ground state dependence on the twist angle has two distinct analytical structures.
AB - The thermodynamic limit of superspin chains can show several intriguing properties, including the emergence of continua of scaling dimensions and the appearance of discrete states when imposing toroidal boundary conditions. Nevertheless, the former’s exhaustive characterization in terms of Conformal Field Theories is still lacking. In order to study the thermodynamic limit of the U_q[sl(2|1)] 3 ⊗ 3̄ superspin chain in the antiferromagnetic regime, we analyze the low lying excitations by means of the model’s exact solution using the Algebraic Bethe Ansatz. In the isotropic limit, this model may be used as a toy model for the description of plateau transitions in Quantum Hall systems. The definition of a quasimomentum operator allows for a characterization of the continua of scaling dimensions, thereby giving rise to a quantum number for the corresponding non-compact component of the spectrum in the thermodynamic limit. The associated degeneracies are lifted on the lattice by logarithmic fine structures. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom, levels from the continuous part of the spectrum flow into discrete levels and vice versa. Investigating the thermodynamic limit of the q-deformed osp(3|2) superspin chain, corresponding to an intersecting loop model in the rational limit, we seek to uncover its low-lying critical exponents. We present evidences that the latter are built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and exponents associated to Z(2) degrees of freedom. This view is supported by the fact that the S = 1 XXZ integrable chain spectrum is present in some of the sectors of the superspin chain at a particular value of the deformation parameter. We find that the fine structure of finite-size effects is very rich for a typical anisotropic spin chain. In fact, we argue on the existence of a family of states with the same conformal dimension whose lattice degeneracies are lifted by logarithmic corrections. On the other hand, we also report on states of the spectrum whose finite-size corrections seem to be governed by a power law behaviour. We finally observe that under toroidal boundary conditions the ground state dependence on the twist angle has two distinct analytical structures.
U2 - 10.15488/8827
DO - 10.15488/8827
M3 - Doctoral thesis
CY - Hannover
ER -