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Topological Orders with Spins and Fermions

Quantum Phases and Computation

  • Laura Ortiz Martín
Book

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Laura Ortiz Martín
      Pages 3-10
    3. Laura Ortiz Martín
      Pages 11-15
  3. Spin Systems

    1. Front Matter
      Pages 17-17
    2. Laura Ortiz Martín
      Pages 19-48
    3. Laura Ortiz Martín
      Pages 49-68
  4. Fermionic Systems

    1. Front Matter
      Pages 69-69
    2. Laura Ortiz Martín
      Pages 71-92
    3. Laura Ortiz Martín
      Pages 93-118
  5. Conclusions

    1. Front Matter
      Pages 119-119
    2. Laura Ortiz Martín
      Pages 121-123
    3. Laura Ortiz Martín
      Pages 125-127
  6. Back Matter
    Pages 129-168

About this book

Introduction

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.

 

Keywords

Symmetry-Enriched Topological Orders Double Semion Model Topological Quantum Computation Non-CSS Topological Code Topological Insulators Rashba Spin-Orbit Coupling Topological Superconductors Majorana Fermions Stability

Authors and affiliations

  • Laura Ortiz Martín
    • 1
  1. 1.Racah Institute of PhysicsThe Hebrew University of JerusalemJerusalemIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-23649-6
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-23648-9
  • Online ISBN 978-3-030-23649-6
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site