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- Rødland, Lukas
(författare)
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Topological Phases of Non-Hermitian physics
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Non-Hermitian physics has introduced phenomena like the skin effect and exceptional points, challenging traditional views of topological phases. This thesis contrasts two classification frameworks for non-Hermitian systems. The first approach employs K-theory classifications based on line-gaps and point-gaps, which explain the topological origins of the skin effect but fail to adequately describe exceptional points. The second, more nuanced approach uses homotopy theory, where the braiding of complex energies around exceptional points is integral to the classification. This method provides a detailed account of the behaviour of exceptional points, such as the splitting and merging of these points. We also study systems restricted by PT-symmetry, a symmetry that ensures that each eigenvalue is real or has a complex conjugate pair, which leads to the formation of an exceptional cone in the parameter space of two-band models. This cone features prominently in the accompanying papers, especially when introducing the concept of non-defective exceptional points and in the homotopy classification of PT-symmetric models.
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| 2. |
- Ortega-Taberner, Carlos, 1993-
(författare)
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Topology off the beaten path : From critical to non-Hermitian systems
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A central topic in condensed matter research during the last decades has been the study and classification of topological phases of matter. Topological insulators in particular, a subset of symmetry protected topological phases, have been investigated for over a decade. In recent years, several extensions to this formalism have been proposed to study more unconventional systems.In this thesis we explore two of these extensions, where key assumptions in the original formalism are removed. The first case is critical systems, which have no energy gap. Conventional topological invariants are discontinuous at topological transitions, and therefore not well-defined for critical systems. We propose a method for generalizing conventional topological invariants to critical systems and show robustness to disorder that preserves criticality. The second case involves non-Hermitian systems, which appear in effective descriptions of dissipation, where we study the entanglement spectrum and its connection to topological invariants. Furthermore, by introducing non-Hermiticity to critical systems we show how the winding numbers that characterize some topological phases of the non-Hermitian system, as well as topological signatures in the entanglement spectrum, can be obtained from the related critical model.
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| 3. |
- Tournois, Yoran, 1991-
(författare)
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Abelian and non-abelian quantum Hall hierarchies
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A core tenet of condensed matter physics has been that different phases of matter can be classified according to Landau's symmetry breaking paradigm. It has become clear, however, that phases of matter exist that are not distinguished by symmetry, but rather by topology. A paradigmatic example of this topological order are the fractional quantum Hall phases, which are the topic of this dissertation. Such phases exhibit the fractional quantum Hall effect, which occurs when electrons confined to two dimensions are subjected to a strong perpendicular magnetic field at very low temperatures. Characterized by a precise quantization of the Hall resistance and a concomitant vanishing of the longitudinal resistance, the fractional quantum Hall effect results from the formation of a strongly correlated quantum liquid of electrons. This quantum liquid supports remarkable quasiparticle excitations, which carry a fractional charge and are thought to obey fractional statistics beyond the familiar Bose-Einstein and Fermi-Dirac statistics.The theoretical understanding of the topological orders realized by the fractional quantum Hall states has progressed by the proposal of explicit trial wave functions as well as various types of effective field theories. This dissertation focuses on two series of trial wave functions, abelian and non-abelian hierarchy wave functions. We study the non-abelian hierarchy wave functions using conformal field theory techniques, by means of which the associated topological properties are studied. These include the fractional charges of the quasiparticles and their non-abelian fractional statistics. In addition, we study abelian hierarchy wave functions using effective Ginzburg-Landau theories in a way that connects to their known conformal field theory description.
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