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Excitations in strict 2-group higher gauge models of topological phases

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  • Published: 17 January 2020
  • Volume 2020, article number 107, (2020)
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Excitations in strict 2-group higher gauge models of topological phases
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  • Alex Bullivant1 &
  • Clement Delcamp  ORCID: orcid.org/0000-0003-2337-57722,3 

  • 502 Accesses

  • 13 Citations

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A preprint version of the article is available at arXiv.

Abstract

We consider an exactly solvable model for topological phases in (3+1) d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.

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Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.

    Alex Bullivant

  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748, Garching, Germany

    Clement Delcamp

  3. Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, München, Germany

    Clement Delcamp

Authors
  1. Alex Bullivant
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  2. Clement Delcamp
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Corresponding author

Correspondence to Clement Delcamp.

Additional information

ArXiv ePrint: 1909.07937

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Bullivant, A., Delcamp, C. Excitations in strict 2-group higher gauge models of topological phases. J. High Energ. Phys. 2020, 107 (2020). https://doi.org/10.1007/JHEP01(2020)107

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  • Received: 25 November 2019

  • Accepted: 15 December 2019

  • Published: 17 January 2020

  • DOI: https://doi.org/10.1007/JHEP01(2020)107

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Keywords

  • Topological States of Matter
  • Anyons
  • Gauge Symmetry
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