Anyonic symmetry and twist defects

Khan, Mayukh Nilay

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https://hdl.handle.net/2142/99304 Copy

Description

Title

Anyonic symmetry and twist defects

Author(s)

Khan, Mayukh Nilay

Issue Date

2017-10-13

Director of Research (if dissertation) or Advisor (if thesis)

Hughes, Taylor L.

Doctoral Committee Chair(s)

Stone, Michael

Committee Member(s)

• Eckstein, James N.
• Peng, Jen-Chieh

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• twist defects
• anyonic symmetry
• anyon condensation
• parafermions
• non-Abelian bound states.

Abstract

Non-Abelian excitations are sought after because of the promise they hold for topological quantum computation. However, in spite of many proposals of systems in which they can occur intrinsically, observation has proved to be elusive. In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.

Graduation Semester

2017-12

Type of Resource

text

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http://hdl.handle.net/2142/99304

Copyright and License Information

Copyright 2017 Mayukh Nilay Khan

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