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

Alex Bullivant (Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.) ; Clement Delcamp (Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, 85748, Germany; Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, München, D-80799, Germany)

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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      "value": "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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Published on:
17 January 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 1
Pages 1-44
DOI:
https://doi.org/10.1007/JHEP01(2020)107
arXiv:
1909.07937
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: