Topological phases in 3+1D: the higher lattice gauge theory model and its excitations
Joe Huxford (Oxford University)
Abstract: Topological phases in 3+1D are less well understood than
their lower dimensional counterparts. A useful approach to the study
of such phases is to look at toy models that we can solve exactly. In
this talk I will present new results for an existing model for certain
topological phases in 3+1D (the model was first presented in [1]).
This model is based on a generalisation of lattice gauge theory known
as higher lattice gauge theory, which treats parallel transport of
lines as well as points. I will first provide a brief introduction to
higher lattice gauge theory and the Hamiltonian model constructed from
it. Then we will look at the simple excitations (both point-like and
loop-like) that are present in this model and how these excitations
can be constructed explicitly using so-called ribbon and membrane
operators. Some of the quasi-particles are confined and we discuss how
this arises from a condensation-confinement transition. We will then
look at the (loop-)braiding relations of the excitations and finish by
examining the conserved topological charges realised by the Higher
Lattice Gauge Theory Model.
[1] A Bullivant, M. Calcada et al., ``Topological phases from higher gauge symmetry in 3+1D", Phys. Rev. B 95, 155118 (2017)
mathematical physics
Audience: researchers in the topic
( video )
Quantum Matter meets Maths (IST, Lisbon)
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Organizers: | João P. Nunes, Jose Mourao*, Pedro Ribeiro, Roger Picken, Vítor Rocha Vieira |
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