Topological phases from higher gauge symmetry in 3+1 dimensions - INSPIRE

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Topological phases from higher gauge symmetry in 3+1 dimensions

Alex Bullivant
(
- Leeds U.
)
,
Marcos Calçada
(
- Leeds U. and
- Ponta Grossa State U.
)
,
Zoltán Kádár
(
- Leeds U.
)
,
Paul Martin
(
- Leeds U.
)
,
João Faria Martins
(
- New Lisbon U.
)

Jun 21, 2016

21 pages

Published in:

Phys.Rev.B 95 (2017) 15, 155118

Published: Apr 13, 2017

e-Print:

1606.06639 [cond-mat.str-el]

DOI:

10.1103/PhysRevB.95.155118

View in:

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Abstract: (APS)

We propose an exactly solvable Hamiltonian for topological phases in 3+1 dimensions utilizing ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a Hamiltonian realization of Yetter's homotopy 2-type topological quantum field theory whereby the ground-state projector of the model defined on the manifold M3 is given by the partition function of the underlying topological quantum field theory for M3×[0,1]. We show that this result holds in any dimension and illustrate it by computing the ground state degeneracy for a selection of spatial manifolds and 2-groups. As an application we show that a subset of our model is dual to a class of Abelian Walker-Wang models describing 3+1 dimensional topological insulators.

Note:

28 pages, 4 figures

phase: topological
symmetry: gauge
Hamiltonian
topological insulator
lattice field theory
partition function
ground state
homotopy
any-dimensional

References(74)

Figures(16)

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