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Title:Methods of Information and Random Matrix Theory in Disordered Topological Materials
Author(s):Basa, Bora
Contributor(s):Gilbert, Matthew
Subject(s):Entanglement spectrum
Disordered topological insulators
Random matrix theory
Abstract:The understanding of the effects of disorder in condensed matter systems has been of great importance at each stage of the development of solid state physics and engineering. This importance has not waned in recent years when the theoretical and experimental study of topological insulators has become one of the most active areas of research in the field. The role of quantum entanglement in these topological phases of matter has also become an exciting frontier of research. In this mostly numerical senior thesis, we explore the methods of random matrix theory along with the established information theoretic framework for probing the topological phase transitions in disordered insulators. Specifically, we seek to understand the spectral properties of the entanglement (modular) Hamiltonian associated with the disordered quantum spin Hall insulator and the p-wave superconducting chain. To this end, we first review the recent developments in the application of random matrix theory methods to the entanglement spectrum and demonstrate the necessary numerical techniques. Guided by these developments, we introduce a new measure, the entanglement participation ratio, to reduce the computational costs of using methods of random matrix theory and provide a theoretical avenue for gaining further physical insight into the entanglement spectrum of disordered topological matter. We find that this new measure is successful in identifying topological phase transitions and in providing a complementary viewpoint to the random matrix theory approach.
Issue Date:2017-12
Date Available in IDEALS:2018-01-31

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