Topological Orders with Spins and Fermions

Quantum Phases and Computation

Laura Ortiz Martín (Autor)

Buch | Hardcover

XVII, 168 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-23648-9 (ISBN)

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This thesis deals with topological orders from two different perspectives: from a condensed matter point of view, where topological orders are considered as breakthrough phases of matter; and from the emerging realm of quantum computation, where topological quantum codes are considered the most appealing platform against decoherence. The thesis reports remarkable studies from both sides. It thoroughly investigates a topological order called the double semion model, a counterpart of the Kitaev model but exhibiting richer quasiparticles as excitations. A new model for symmetry enriched topological order is constructed, which adds an onsite global symmetry to the double semion model. Using this topological phase, a new example of topological code is developed, the semion code, which is non-CSS, additive, non-Pauli and within the stabiliser formalism.
Furthermore, the thesis analyses the Rashba spin-orbit coupling within topological insulators, turning the helical edge states into generic edges modes with potential application in spinstronics. New types of topological superconductors are proposed and the novel properties of the correspondingly created Majorana fermions are investigated. These Majorana fermions have inherent properties enabling braiding and the performance of logical gates as fundamental blocks for a universsal quantum computator.

Until now, Laura Ortiz Martin's career has been a purely scentific, although she has addressed topics which could be very useful for entrepreneurial environment nowadays, focusing in Quantum Technologies. She obtained her first degree and M.Sc in Madrid, at the Universidad Complutense, then continued her research at CSIC, the National Research Institute, before returning to the Universidad Complutense to for her Ph.D. During her doctoral studies , she attended many international conferences and visited numerous research groups around the world. Currently, she is a Postdoctoral Fellow at the Hebrew University of Jerusalem.

Introduction.- Topology in Condensed Matter.- Topology in Quantum Information.- Spin systems.- The bilayer double semion model.- Double semion model as a quantum memory .- Fermionic systems.- Topological insulators.- Topological superconductors.- Conclusions and appendices.

Erscheinungsdatum	26.07.2019
Reihe/Serie	Springer Theses
Zusatzinfo	XVII, 168 p. 65 illus., 56 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	439 g
Themenwelt	Naturwissenschaften ► Chemie ► Analytische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
Schlagworte	Double Semion Model • Majorana Fermions Stability • Non-CSS Topological Code • Rashba Spin-Orbit Coupling • Symmetry-Enriched Topological Orders • Topological Insulators • topological quantum computation • Topological superconductors
ISBN-10	3-030-23648-X / 303023648X
ISBN-13	978-3-030-23648-9 / 9783030236489
Zustand	Neuware